2015年度
- 2016/3/28 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Hideyuki Mizuno (Fukui Institute for Fundamental Chemistry)
- Title
- Vibrational excitations and elastic heterogeneities in disordered solids
- Outline
- What makes the difference when sound propagation is investigated in a crystal or in a glass? One hundred years ago, Debye rationalized the former case in terms of phonons. In contrast, years of effort have failed to provide a convincing picture for vibrations in glasses. A feature of glasses is their inhomogeneous mechanical response at the nano-scale, i.e. some regions are sensibly softer than others. These “elastic heterogeneities" should interfere with the vibrational excitations supported by the material which, in contrast to he case of perfect crystal, cannot be completely described in terms of phonons.
We provide a contribution to this issue by molecular dynamics simulations of a toy model, which interpolates from the perfect crystal case, through increasingly defective phases, to fully developed glasses, in a unified framework. By calculating appropriate dynamical structure factors, we have demonstrated a direct correlation between soundwaves features and the heterogeneous mechanical response at the nano-scale. The findings also apply to heat transfer, a discovery that could help in the design of better thermoelectric materials. The symmetry and order of the materials' nanostructure can be optimized to minimize the transfer of heat.
- 2016/3/2 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Etienne Fodor (Paris Diderot University - Paris 7)
- Title
- Self-propelled particles as an active matter system
自己泳動粒子からなる活性物質系の性質
- Outline
- In the realm of active matter, the particles' motion is driven by external
energy sources. Self-propulsion alone, which occurs in many experimental
realizations, leads to a rich phenomenology that cannot be accounted for by
equilibrium physics arguments.
On a specific model of self-propelled particles, I will explore how far from
equilibrium its dynamics operate. I will also show that some concepts inherited
from equilibrium physics may nevertheless have their say.
- 2016/2/24 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Anki Reddy Katha (Indian Institute of Technology, Gowahati)
- Title
- Molecular Dynamics Investigation of Polymer membranes and polyelectrolytes
- Outline
- Molecular dynamics simulation was employed to study the effect of inclusion of polyoctahedral oligomeric silsequioxanes (POSS) into the active layer of polyamide (PA) thin film composite membrane which resulted in higher water flux and salt rejection than pure PA membranes. Quantities, such as water diffusivity, water partition coefficient, fractional free volume and range of free volume size computed on the equilibrated configurations, increased on the inclusion of POSS in PA membranes. Moreover salt diffusivity was lower in PA-POSS than PA. Therefore from the simulation study, it was concluded that the introduction of POSS into PA membrane improved (a) porosity of composite membrane, (b) hydrophilicity and (c) charge on the membrane. These effects explain the increase of water flux and salt rejection in nanocomposite membranes.
The use of forward osmosis (FO) process for seawater desalination has attracted tremendous interest in recent years. Besides the manufacture of suitable membranes, the major technical challenge in the efficient deployment of the FO technology lies in the development of a suitable "draw solute". Poly electrolytes could be one such system to be used as a draw solute apart from switchable salts, inorganic salts and others. We explored the dynamics of poly(aspartic acid) and its sodium salt in the dilute concentration regime to comment on its applicability as a draw solute by quantification of the polymer conformational properties, its solvation behavior, and the counterion dynamics. The neutral polymer shows a preferentially coiled structure whereas the fully ionized polymer has an extended structure. Upon comparing with poly(acrylic acid) polymer, another polymer which has been used as a draw solute, poly(aspartic acid) forms more number of hydrogen bonds as well as fewer ion pairs.
- 2016/2/22 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Daisuke Mizuno (Kyushu Univ.)
水野 大介 (九州大学)
- Title
- Non-Gaussian limit distributions out of truncated power-law interactions
丸められた冪乗相互作用による非ガウス極限分布
- Outline
- Nature is full of power-law interactions, e.g., gravity, electrostatics, and
hydrodynamics. When sources of such interactions are distributed in space, the
superposed interaction, which is what we observe, is naively expected to follow
a Gauss or Levy distribution. Here, we show that the actual distribution of
physical observables frequently converges to something in between these limit
distributions. We present an analytical expression that bridges, continuously,
the gap between them, depending on physical parameters, such as the
concentration of sources and the size of the probe. By comparing with numerical
simulations, the origin of non-Gauss and non-Levy distributions are
theoretically articulated.
We then show that the derived non-Gauss distribution, which we call as
Truncated Levy for simplicity, can be observed in various out-of-equilibrium
systems including bacterial bath, active cytoskeletons, and possibly turbulence
and glass. We investigated the probability distribution of probe fluctuations
dispersed in suspensions of swimming microorganisms, and active cytoskeletons.
Being heavily tailed, they converged to Truncated Levy distribution in a manner
quantitatively predictable with experimentally controllable parameters, such as
concentrations, probe sizes. Not only the short-term displacements but also
their time-evolution showed universal collapse when normalized. Investigating
its origin instructed us the unexpectedly broader applicability of the theory
that neglects near-field interactions.
- 2016/2/17(Wed)_2/19(Fri) - @Seminar Room K206, Yukawa Institute
- Speaker
- Hajime Yoshino (Cybermedia Center, Osaka University)
- Title
- Statistical mechanics of glass/jamming systems: the replica method and its applications
- Outline
- In these lectures we discuss a 1st principle, statistical mechanical approach to glass/jamming systems. Glasses which are as rigid as crystals and as disordered as liquids can be found in broad range of systems ranging from soft matters such as colloids and polymers to hard matters such as metallic compounds. They remained out of reach for physicists for a long time but recently the ideas and skills developed in the statistical mechanics of quenched disordered system are found to provide useful clues and powerful tools to analyze glasses without quenched disorder.
First we discuss a class of extended mean-field spinglass models which play the role of prototypes to develop theories of glass/jamming systems. The replica method will be explained in detail. Then we show how one can extend the approach to analyze glassy systems without quenched disorder. In particular we discuss the density functional theory for replicated liquid which is currently under rapid development. We focus especially on the hardspheres in large dimensional limit for which exact computations are possible. Finally we discuss more recent results based on this approach. The lectures will be given on the blackboard with occasional use of slides.
Feb.17, 10:30-12:00, 13:30-15:00, 15:30-17:00
1) Introduction
2) Random energy model and p-spin spinglass models
3) Replica symmetric solution and 1 step replica symmetry breaking
Feb.18, 10:30-12:00, 13:30-15:00, 15:30-17:00
1) Connections to dynamics
2) Density functional theory of liquids
3) Basic ideas of replicated liquid theory
Feb.19, 10:30-12:00, 13:30-15:00, 15:30-17:00
1) Hardspheres in large-d limit : 1RSB and dynamic/static glass transitions
2) Hardspheres in large-d limit: continuous RSB and jamming criticality
3) Glass state following under compression/shear
4) Outlook
- 2016/2/10 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Andrea Cairoli (Queens Mary University, London)
- Title
- Anomalous processes with general waiting times: Functionals,
Multipoint Structure and the role of Galilean invariance.
- Outline
- Continuous-Time random walks (CTRWs) have been successfully used to
model subdiffusive biological processes, characterized by a sublinear
power-law scaling of the mean square displacement, thus pushing
research both on their application to experiments and on the
development of their mathematical formalism.
However, different questions still remain unsolved. On the one hand,
many transport processes in biological systems have recently been
found exhibiting more complex anomalous diffusive behavior, where
typically crossovers between different scaling regimes appear over
time, which cannot be modeled by CTRWs. On the other hand, the
analytical treatment of more realistic setups, which would allow to
investigate further properties of these processes, for instance their
stochastic thermodynamics, has not yet been achieved.
In this talk, we will present recent advances on both these two
issues. We will first discuss a class of anomalous diffusion
processes, which is able to capture more complex dynamical behavior,
by extending the usual CTRWs to more general waiting time
distributions. We will present the complete characterization of their
functionals and multipoint structure, by using a representation in
terms of a normal diffusive process plus a stochastic time change. We
will then discuss the breaking of Galilean invariance for CTRWs and
introduce new weakly anomalous processes, preserving it. The relation
of this problem with the stochastic thermodynamics framework will then
be discussed.
- 2016/2/3(Wed)_2/5(Fri) - @Seminar Room K206, Yukawa Institute
- Speaker
- Frederic van Wijland (Universite Paris Diderot)
- Title
- Quantum methods for stochastic dynamics
- Outline
- Lecture 1(Feb.3. 13:30-15:00)
Stochastics dynamics. Master equation, Fokker-Planck, Langevin. Itô
vs. Stratonovitch. Martin-Siggia-Rose-Janssen-De Dominicis path
integral formulation.
Lecture 2(Feb.3, 15:15-16:30)
Reversibility, irreversibility, entropy production, Gallavotti-Cohen
theorem, linear response, Fluctuation-Dissipation theorem.
Supersymmetry and its uses in classical stochastics dynamics.
Lecture 3(Feb. 4, 13:30-15:00)
Many-body problems and quantum spin chains, interacting fermions and
interacting bosons. Kinetic Ising model.
Lecture 4(Feb. 4, 15:15-16:30)
Nonequilibrium phase transitions and critical phenomena. Field
theoretic methods. Doi-Peliti.
Lecture 5(Feb. 5, 13:30-15:00)
Fluctuating hydrodynamics of diffusive systems. WKB method. The Simple
Symmetric Exclusion Process.
Lecture 6(Feb.5, 15:15-16:00)
Dynamical large deviations in classical systems and quantum phase transitions.
- 2016/1/27 (Wed) 16:30 - @Seminar Room K102, Yukawa Institute
- Speaker
- Michio Otsuki (Shimane Univ.)
大槻 道夫 (島根大学)
- Title
- Shear modulus of granular materials under oscillatory shear near
jamming transition
ジャミング転移点近傍での粉体の剪断剛性率
- Outline
- Granular materials have rigidity above a critical volume fraction,
while they lose rigidity below it. Such rigidity transition, known as
the jamming transition, has attracted much attention among researchers
in these days. It is well known that shear modulus under infinitesimal
shear satisfies a scaling relation near the jamming point
[1]. However, a recent experiment [2] suggests that the shear modulus
obeys a different scaling law where the critical exponent differs from
that in Ref. [1]. What we propose is that the conflict in the previous
works can be resolved by considerations of the stress avalanches which
take place in the process of large amplitude shear strains. In fact,
it is known that a large strain breaks bonds between contacting grains
and causes slip avalanches distributed in a broad range of sizes [3].
To interpolate previously reported relations, we postulate a critical
scaling law, which is confirmed by our numerical simulation of
frictionless particles [4]. In addition, we phenomenologically
determine the values of the critical exponents in the critical scaling
law. In this presentation, we also present the detailed results on the
behavior of shear modulus for frictional granular particles.
It is found that the critical exponents to characterize the jamming
transition discontinuously change if there exists infinitesimal
friction between grains. The origin of the discontinuity is discussed.
[1] C. S. O’Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Phys.
Rev. Lett. 88:075507, 2002.
[2] C. Coulais, A. Seguin, and O. Dauchot, Phys. Rev. Lett. 113:198001, 2014.
[3] K. Dahmen, D. Ertas ?, and Y. Ben-Zion, Phys. Rev. E 58:1494, 1998.
[4] M. Otsuki and H. Hayakawa, Phys. Rev. E 90:042202, 2014.
- 2015/12/16 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Adrian Baule (Queen Mary University of London)
- Title
- Optimal escape from metastable states driven by non-Gaussian noise
非ガウスノイズによる準安定状態からの遷移
- Outline
- A fundamental understanding of the dynamics of systems under the influence of
thermal fluctuations is provided by investigating its large deviation properties
in the limit of weak noise strength. This approach has provided, for example,
theories of activated escape in low temperature regimes and is also intimately
linked to the description of quantum mechanical systems within a semiclassical
approximation. However, many complex systems are driven by non-thermal (active)
fluctuations with non-Gaussian characteristics. Here, we investigate the
weak-noise limit of systems driven by non-Gaussian noise using a path-integral
approach. We apply this approach to the problem of escape from a metastable
potential. Exact results for the weak-noise asymptotics of Kramer's escape rate
and the optimal escape paths are obtained.
- 2015/12/14 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Yasuhiro Utsumi (Mie University)
内海 裕洋 (三重大学)
- Title
- Fluctuation Theorem for a Small Engine and Magnetization Switching by Spin Torque
微小熱機関の揺らぎの定理とスピントルク磁化反転
- Outline
- We consider a reversal of the magnetic moment of a nano-magnet by the
fluctuating spin-torque induced by a non-equilibrium current of electron spins.
This is an example of the problem of the escape of a particle from a metastable
state subjected to a fluctuating non-conservative force [1]. The spin-torque is
the non-conservative force and its fluctuations are beyond the description
of the fluctuation-dissipation theorem. We estimate the joint
probability distribution of work done by the spin torque and the Joule
heat generated by the current, which satisfies the fluctuation theorem
for a small engine. We predict a threshold voltage above which the
spin-torque shot noise induces probabilistic switching events and below
which such events are blocked. We adopt the theory of the full-counting
statistics under the adiabatic pumping of spin angular momentum. This
enables us to account for the backaction effect, which is crucial to
maintain consistency with the fluctuation theorem.
[1] Yasuhiro Utsumi and Tomohiro Taniguchi Phys. Rev. Lett. 114, 186601
(2015).
- 2015/11/18 (Wed) 16:00- @Seminar Room K102, Yukawa Institute
- Speaker
- Takafumi Suzuki (Univ. of Tokyo)
鈴木貴文 (東京大学)
- Title
- Functional renormalization group study of the current noise of the interacting resonant level model
汎関数くりこみ群法による相互作用共鳴準位模型の電流ゆらぎの解析
- Outline
- Remarkable advance in nanotechnology opens up the possibility to explore
nonequilibrium transport in experimentally well-controlled situations. The
interacting resonant level model (IRLM) is an archetypical example to describe a
single-level quantum dot dominated by charge fluctuations which are affected by
the local two-particle interaction of dot and lead fermions. What is remarkable
transport property of the IRLM is that universal features appear in its I-V
characteristic when the lead band-width is much larger than any other energy
scale. In this scaling regime, the current at large bias voltage is suppressed
following a power law, whose exponent depends on the strength of the local
interaction[1]. While a unified picture for the current of the IRLM has been
established by various methods, little is known about its fluctuation except for
a special symmetric point[2]. As the current noise is known to contain rich
information on the nonequilibrium transport, it is strongly
desirable to develop a systematic framework to calculate the current noise and
its full counting statistics in general parameter regimes.
In this seminar, I will discuss the zero-frequency current noise of the IRLM for
arbitrary bias voltages using a functional renormalization group approach[3]. We
extend the existing nonequilibrium scheme by deriving and solving flow equations
for current-vertex corrections. Artificial divergences of the current noise
found in lowest-order perturbation theory in the two-particle interaction are
consistently removed using our renormalization scheme. This allows us to gain a
comprehensive picture of the current noise in the scaling limit.
[1] B. Doyon, PRL 99, 076806 (2007)
[2] A. Branschaedel, E. Boulat, H. Saleur, and P. Schmitteckert, PRL 105, 146805 (2010)
[3] C. Karrasch, M. Pletyukhov, L. Borda, and V. Meden, PRB 81, 125122 (2010)
- 2015/11/16 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Werner Krauth (Ecole normale superieure)
- Title
- Two-dimensional melting: New algorithms, new insights
2次元融解:新しいアルゴリズム、新しい見識
- Outline
- The hard-disk model has exerted outstanding influence on computational
physics and statistical mechanics. Decades ago, hard disks were the
first system to be studied by Markov-chain Monte Carlo methods [1] and
by molecular dynamics [2]. It was in hard disks, through numerical
simulations, that a two-dimensional melting transition was first seen to
occur [3] even though such systems cannot develop long-range crystalline
order. Analysis of the system was made difficult by the absence of
powerful simulation methods.
In recent years, we have developed powerful Monte Carlo algorithms for
hard disks and related systems [4] which allowed us to prove [5] that
hard disks melt with a first-order transition from the liquid to the
hexatic and a continuous transition from the hexatic to the solid. I
will finally discuss how the event-chain algorithm overcomes the
limitations of the Metropolis algorithm [6], even for general
potentials, and on the insights it allows on the the generic theory of
two-dimensional melting [7].
References:
[1] N. Metropolis,, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E.
Teller, J. Chem. Phys. 21 1087 (1953).
[2] B. J. Alder and T. E. Wainwright, J. Chern. Phys. 27,1208 (1957).
[3] B. J. Alder and T. E.Wainwright, Phys. Rev. 127, 359 (1962).
[4] E. P. Bernard, W. Krauth, D. B. Wilson Phys.Rev. E 80 056704 (2009).
[5] E. P. Bernard, W. Krauth Phys. Rev. Lett. 107, 155704 (2011).
[6] M. Michel, S. C. Kapfer, W. Krauth J. Chem. Phys. 140 54116 (2014).
[7] S. C. Kapfer, W. Krauth Phys. Rev. Lett. 114, 035702 (2015).
- 2015/11/11 (Wed) 16:00- @Seminar Room K206, Yukawa Institute
- Speaker
- Shiwani Singh (Kyushu Univ.)
- Title
- Lattice Fokker Planck Method for Complex Fluids
格子フォッカープランク法を用いた複雑流体の解析
- Outline
- In the last two decades, the lattice Boltzmann method (LBM) has emerged as an
alternate tool to simulate the hydrodynamics of Newtonian fluids. The lattice
Boltzmann method can be understood as approximate discrete technique for solving
Boltzmann BGK equation. We present a mechanism which only relies on BGK
relaxation description to reproduce viscoelastic behavior. Basically, for
numerical convenience, the actual diffusive dynamics in momentum space, which is
described by Fokker Planck equation, is replaced by relaxation dynamics of the
BGK type. Applying the lattice Boltzmann formulation to the resulting kinetic
equations with a BGK relaxation term, we determine the bulk rheological
properties for two canonical flow situations viz. simple shear and extensional
flows. Further, in order to extend the scheme for non-homogeneous flows, the
system is modeled as two component mixture consisting of polymer dumbbells and
solvent gas. This system is contrasted with the gaseous mixture case where the
Boltzmann type kinetic models are well developed. An extension of two component
Boltzmann equations and associated models are developed for polymer-solvent
mixture case. The model is then validated numerically for the case of one way
coupling with the imposed plane Poiseuille flow.
- 2015/11/4 (Wed) 16:00- @Seminar Room K102, Yukawa Institute
- Speaker
- Taiki Haga (Kyoto University)
芳賀大樹(京都大学)
- Title
- Non-equilibrium quasi-long-range order of a driven random field O(N) model
ランダム場中を駆動されるO(N)モデルにおける準長距離秩序
- Outline
- How quenched disorder affects the nature of phase transition
has been a main topic of intensive research in statistical
physics [1]. The random field Ising model and the spin glass
models are examples of well-studied disordered systems.
On the other hand, the presence of non-conservative external
forces, which drive the system out of equilibrium, can also
alter the nature of phase transition [2]. For example, it is
known that the steady shear changes the critical exponents
of critical fluids.
In this study, we ask what kind of phase transition occurs
in the presence of both quenched disorder and driving force.
As the simplest phase ordering systems that contain disorder
and driving, we investigate three-dimensional O(N) spin models
driven with a uniform velocity over a random field. We show that
the models with N=2 and 3 exhibit quasi-long-range order
(QLRO), in which the spatial correlation function decays in
a power-law form, at low temperatures and that the transition
from the QLRO phase to the disordered phase resembles the
Kosterlitz-Thouless (KT) transition in the two-dimensional pure
XY model in equilibrium. This "non-equilibrium KT transition"
may define a novel type of universality class, wherein the
interplay between disorder and driving plays a crucial role [3].
[1] Spin Glasses and Random Fields, edited by A.P. Young (World Scientific, Singapore, 1998).
[2] Phase Transition Dynamics, A. Onuki (Cambridge University Press, 2007).
[3] T. Haga, arXiv:1504.06411.
- 2015/10/26 (Mon) 16:00- @Seminar Room K206, Yukawa Institute
- Speaker
- Ken Funo (Univ. of Tokyo)
布能 謙 (東京大学)
- Title
- Work fluctuation-dissipation trade-off in heat engines
- Outline
- Recent developments of nonequilibrium statistical mechanics allow us to
formulate thermodynamic relations for arbitrary nonequilibrium initial and
final states [1]. They can be used to quantify thermodynamic costs of
information encoding and erasure processes as well as to quantify the
extractable work from information heat engines. In those general situations,
reducing energy dissipation allows us to increase the efficiency of a given
thermodynamic task, and reducing work fluctuation allows us to inject into
the system an exact amount of work needed to complete the task, or to
extract a deterministic amount of work from the system. Thus, suppressing
both work fluctuation and energy dissipation is vital to control nanosystems
that work at the level of thermal fluctuations.
Previous studies have explored the regime around vanishing work fluctuations
by using techniques of quantum information theory, known as the single-shot
statistical mechanics [2, 3] and the regime around vanishing energy
dissipation by using the second law of thermodynamics [1]. However, as we
prove in the present work, these two aims are incompatible. We derive the
fundamental trade-off relation between work fluctuation and energy
dissipation in heat engines starting from and ending at arbitrary
nonequilibrium states and that the lower bound is quantified by the degree
of nonequilibriumness of the initial and final states as measured in terms
of the information distance [4]. We propose a method to construct explicit
protocols that achieve the lower bound of the trade-off relation. An
application of the trade-off relation to information heat engines is carried
out, including a numerical simulation to test the trade-off relation.
[1] M. Esposito and C. Van den Broeck, Euro. Phys. Lett. 95, 40004 (2011).
[2] J. Aberg, Nat. Commun. 4, 1925 (2013).
[3] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
[4] K. Funo and M. Ueda, arXiv:1508.04042.
- 2015/10/21 (Wed) 16:00- @Seminar Room K202, Yukawa Institute
- Speaker
- Kotaro Otomura (Univ. of Tokyo)
乙村浩太郎 (東京大学)
- Title
- Internal Structure and Non Linear Rheology of Non Brownian Suspension with Low Reynolds Number Fluid
低レイノルズ数非ブラウン粒子懸濁液の内部構造と非線形性粘弾性の関係
- Outline
- The suspension, which is one of the complex fluid consist of fluid and
another phase, can show the variety of the complex behaviors, e.g.,
shear thickening/thinning or plastic behavior. The complex fluid are
ubiquitous in the nature, but it's hard to find the microscopic
description of their macroscopic behaviors due to its complexity.
In this seminar, I will focus on the the non-Brownian suspension with
the low Reynolds number fluid, and give some numerical result about the
relationship between the distribution of particles and the rheology. And
I also discuss about the simple model which can partly reproduce the
rheology of them including the nonlinear behavior.
- 2015/9/14 (Mon) 16:00- @Seminar Room K206, Yukawa Institute
- Speaker
- Masaru Hongo (Univ. of Tokyo, RIKEN)
本郷優 (東京大学, 理研)
- Title
- Derivation of relativistic hydrodynamics from quantum field theory
場の量子論に基づいた相対論的流体力学の導出
- Outline
- Hydrodynamics is a low-energy effective theory which describes a long-distance
and long-time behavior of many-body systems. It is applicable not only to a
non-relativistic weakly-interacting dilute gas but also a relativistic
strongly-interacting dense liquid such as the quark-gluon plasma created in
heavy-ion collisions. Although relativistic hydrodynamics itself is
well-established formalism, its derivation from underlying microscopic theories,
or quantum field theories, remains to be completely elucidated.
In this study, considering the recent development of non-equilibrium statistical
mechanics [1], we derive the relativistic version of the Navier-Stokes equation
from the point of view of quantum field theories [2]. In order to derive the
hydrodynamic equation, we put an assumption that the local Gibbs distribution is
realized at initial time, and perform derivative expansions. As a result, we
derive the first-order constitutive relations with the Green-Kubo formulas for
the transport coefficients. We also show that zeroth-order constitutive
relations comes from the thermodynamic potential for local Gibbs distribution,
which is described by the language of quantum field theories in “curved spacetime”.
[1] S.-i. Sasa, Phys. Rev. Lett 112, 100602 (2014).
[2] T. Hayata, Y. Hidaka, M. Hongo, and T. Noumi, arXiv: 1503.04535 [hep-ph].
- 2015/9/9 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Koshiro Suzuki (CANON Inc.)
鈴木功至郎 (キヤノン(株))
- Title
- Theory for Divergent Viscosity in Jammed Granular Materials
ジャミング粉体の粘性率発散の理論
- Outline
- Jamming transition is an athermal phase transition of amorphous solids, which
is characterized by the divergence of the viscosity, or the emergence of the
rigidity. This phenomenon is universely observed in disordered materials such as
colloidal suspensions, emulsions, foams, as well as granular materials, and has
been extensively investigated by experiments, numerical simulations, or
phenomenologies. As for the theoretical approach, it has been controversial
whether the framework of statistical mechanics is valid for its description, due
to its athermal nature, i.e. genuinely nonequilibrium nature. Boltzmann-Enskog
kinetic theory for inelastic spheres or disks is the unique microscopic theory
established so far for granular flows [1]. However, it is recognized that this
theory is invalid for dense granular materials above volume fraction 0.5.
The obstacle in applying statistical mechanics to athermal, nonequilibrium
phenomena resides in the difficulty for obtaining an explicit expression of the
distribution function. We propose a novel microscopic theory starting from the
Liouville equation, equivalent to the Newton's equation, to obtain an explicit
approximate expression for the steady-state nonequilibrium distribution function
for weakly sheared and dissipative cases. Analytic formulas for the steady-state
shear stress (viscosity) and the granular temperature are obtained from this
distribution function, which exhibit a divergence in the vicinity of the jamming
point. It has been confirmed that the formulas agree well with the result of the
MD simulation up to the jamming density. This formulation is consistent with the
conventional linear response theory around equilibrium, and reduces the problem
to the one of equilibrium statistical mechanics with an effective Hamiltonian [2].
[1] J.T.Jenkins and M.W.Richman, Arch.Rat.Mech.Anal.87, 355 (1985); V.Garzo and
J.W.Dufty, Phys.Rev.E 59, 5895 (1999).
[2] K.Suzuki and H.Hayakawa, Phys.Rev.Lett.115, 098001 (2015).
- 2015/7/15 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Takafumi Suzuki (Tokyo Univ.)
鈴木貴文(東京大学)
- Title
- Photon-assisted current noises through a quantum dot system
振動外場下の量子ドット系における電流ゆらぎ
- Outline
- Photon-assisted transport through mesoscopic conductors has attracted much attention because the quantum nature of transport processes is significantly modified by time-dependent fields[1].
In recent years, the scattering theory has revealed that current noises provide information about the photon-assisted transport of noninteracting electrons.
For example, Levitov and Lesovik showed that photon-assisted current noises can detect the phase of the transmission amplitudes induced by the external time-dependent field [2].
Studying the effect of the Coulomb interaction is an important next step to discuss interesting physics, such as the Coulomb blockade and the Kondo effect.
In this talk, I will discuss the photon-assisted transport in an interacting quantum dot system under a periodically oscillating gate voltage [3].
Photon-assisted current noises in the presence of the Coulomb interaction are calculated based on a gauge-invariant formulation of time-dependent transport.
The behavior of the vertex corrections under the AC field will be discussed within the self-consistent Hartree-Fock approximation.
The present result provides a useful viewpoint for understanding photon-assisted transport in interacting electron systems.
[1] G. Platero and R. Aguado, Phys. Rep.395, 1 (2004)
[2] G. B. Lesovik and L. S. Levitov, PRL 72, 538 (1994)
[3] T. J. Suzuki and T. Kato, PRB 91, 165302 (2015)
- 2015/7/8 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Shunji Matsuura (Kyoto Univ.)
松浦 俊司(京都大学)
- Title
- Mean-field analysis of quantum annealing correction
平均場解析を用いた量子アニーリング誤り訂正
- Outline
- Quantum annealing provides a robust method to perform quantum computation.
While its theoretical framework is less understood compared to the quantum gate
model's, it is remarkable that this algorithm has already been
used in commercial quantum machines for solving combinatorial optimization
problems.
In order to solve practically interesting problems, the number of qubits has to
be large.
The current quantum annealing processors (D-wave machines) use 512 qubits. This
number has been increased significantly
in the past years and will be increased in the near future.
As the size of the quantum system becomes larger,
quantum error becomes a more significant problem.
Quantum error in quantum annealing is deeply related to
its time dependent process.
Recently there was a proposal for quantum error correction in quantum annealing.
D-wave experiments show positive results for this error correction method.
In this talk I will explain how and why the quantum annealing correction works
from statistical physics point of view.
- 2015/7/1 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Yui Kuramochi (Kyoto Univ.)
倉持結 (京都大学)
- Title
- Minimal sufficient positive-operator valued measures
最小十分な正作用素値測度
- Outline
- Positive-operator valued measure (POVM) is a mathematical object
that describes the measurement outcomes for
general quantum measurement processes.
For the price of the generality,
some POVMs include redundant information irrelevant to
the measured quantum system
and also there exist many POVMs which have the information
equivalent to a given POVM.
In this talk, we introduce a concept of
a minimal sufficient POVM,
which is the least redundant POVM
among the POVMs that give the same information
about the system.
We also show that
there exists a minimal sufficient POVM
equivalent to a given POVM
and that such POVM is unique up to relabeling.
- 2015/06/24 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Atsushi Ikeda (Kyoto Univ.)
池田 昌司 (京都大学)
- Title
- Glass transition of ellipsoids -- A microscopic theory study
楕円体系のガラス転移 -- 微視的理論からのアプローチ
- Outline
- When the crystallization is avoided, the dynamics of liquids slows drastically
and finally liquids become amorphous solids, which is known as the glass
transition. In experimental studies, the wide varieties of glass-forming systems
have been studied and their glass transitions are revealed to have rich
phenomenologies [1]. On the other hand in theoretical studies, in order to keep
the analysis tractable, the simplified models, such as hard spheres, have been
focused. Recentlly, we have been working to bridge these theoretical and
experimental efforts, by extending the microscopic mean-field theory of the
glass transition to more complicated systems. In particular we focus on the
replica theory [2], that is the theory to calculate the structures and
thermodynamics of supercooled liquids and glasses through a replication of
systems. In this talk, we develop a replica theory of the glass transition of
ellipsoids to discuss the effect of particle's anisotropy on the glass
transition. We use the techniques of molecular liquis state theory [3] to take
into account particle's orientation. We shows the theory reproduces well the
fact that the transition density is strongly dependent on the aspect ratio of
ellipsoids.
[1] C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMillan, and S. W. Martin,
J. Appl. Phys. 88, 3113 (2000).
[2] G. Parisi, and F. Zamponi, Rev. Mod. Phys. 82, 789 (2010).
[3] C. G. Gray, and K. E. Gubbins, Theory of Molecular Fluids: I: Fundamentals
(Oxford, UK, 1984).
- 2015/06/22 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Satoshi Takada (Kyoto Univ.)
髙田 智史 (京都大学)
- Title
- Kinetic theory for dilute cohesive granular gases with a square well potential
井戸型ポテンシャルをもつ稀薄引力粉体系の運動論
- Outline
- The hydrodynamic description of granular materials is useful to know the
rheological properties of the granular flow. Since granular materials are
recognized to behave as unusual solids, liquids and gases, granular materials
have attracted much interest among physicists. If the kinetic energy or the
granular temperature of a granular gas homogeneously decreases the granular
temperature or the kinetic energy of granular gas due to inelastic collisions
between grains, the time evolution of the temperature obeys Haff's law. However,
this homogeneous cooling state cannot be maintained as time goes on, because
clusters of dense region appear as the effect of inelastic collisions. Such
inhomogeneity of granular gases can be understood by granular hydrodynamics in
which the transport coefficients for the inelastic hard core system for the
dilute case and the moderate dense case can be determined by the inelastic
Boltzmann-Enskog equation.
For fine powders or we granular systems, however, cohesive force cannot be
ignored. The ordinary kinetic theory for a hard core system cannot be applied to
this system. We develop the kinetic theory of dilute cohesive granular gases in
which the attractive part is described by a square well potential. We derive the
hydrodynamic equations from the kinetic theory with the microscopic expressions
for the dissipation rate and the transport coefficients. We check the validity
of our theory by performing the direct simulation Monte Carlo.
- 2015/06/15 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Jaeha Lee (Tokyo Univ.)
李 宰河 (東京大学)
- Title
- Modelling Quantum Measurement under Uncertainty
「不確かな量子測定」の記述について
- Outline
- It is widely recognised that "imperfection" is practically unavoidable
in any measurements, and quantum measurements are no exception. Sources of
imperfection range from those of various technical origins such as precision
limit of measuring devices, up to those that may have more subtle roots such as
ill-definedness of the measurand, subjectivity of the observer or even the limit
of human recognition. In awareness of its omnipresence and overwhelming
abundance, it is considered virtually impossible, either in principle or in
practice, to perfectly track down all such causes of imperfection, and still
less, to cast them in a statistical model and precisely evaluate their effects.
Modern metrology has been conscious of this issue, and the subtlety of its
nature is documented in detail under the guidelines GUM [1] and VIM [2], in
which the imperfections concerned are collectively termed "measurement uncertainty."
With today's improvement in technology, honest evaluation of measurement
uncertainty and accurate estimation of its aftermaths are becoming increasingly
important. However, the concept of uncertainty and the subtleties inherent in it
is far from being well recognised among the physics community including quantum
metrology. Even in the aforementioned guidelines, the mathematics for handling
uncertainty, especially for systems that behave probabilistically such as
quantum systems, seems rather premature and lacks a unified or axiomatic
mathematical framework.
In this talk, we first introduce the fuzzy probability theory [3-4], which is a
proposal for the generalisation of the standard Kolmogorovian probability theory
by relaxing some of its axioms, as the central mathematical framework within
which we attempt to model measurement under uncertainty. Subsequently, by
recalling how the standard quantum measurement theory is build upon the basic
concepts of probability theory, we shall see how this generalised framework may
enable the description of "quantum measurements under uncertainty."
As its primary field of application, we then refer to the study on the advantage
of the post-selection technique (or, the so-called "weak measurement") which has
recently caught wide attention due to the conflicting claims coming from two
distinct, but complementary, perspectives of experimental physicists [5] and
statisticians [6]. We shall see that our framework reconciles this apparent
conflict by
showing that the essence of the post-selection technique lies in taking
advantage of the trade-off relation between signal amplification effect and
statistical deterioration [7].
[1] Joint Committee for Guides in Metrology: Guide to the expression of
uncertainty in measurement, JCGM 100 (2008).
[2] Joint Committee for Guides in Metrology: International vocabulary of
metrology - Basic and general concepts and associated terms, JCGM 200 (2008).
[3] G. Choquet, Annales de l'Institut Fourier 5: 131?295 (1953).
[4] M. Sugeno, Ph.D. thesis. Tokyo Institute of Technology, Tokyo, Japan (1974).
[5] O. Hosten and P. Kwiat, SCIENCE, 319, 787?790 (2008).
[6] S. Tanaka and N. Yamamoto, Phys. Rev. A, 88(042116) (2013).
[7] J. Lee and I. Tsutsui, Quantum Studies: Mathematics and Foundations, 1,
65-78 (2014).
- 2015/06/10 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- John Molina (Kyoto Univ.)
- Title
- Rheology of Colloidal Dispersions using the Smooth Profile Method
- Outline
- We show how the Smooth Profile Method can be used to study the dynamics of particle dispersions under shear flow with fully resolved hydrodynamics. The proposed method is applicable to complex non-Newtonian host fluids, high Reynolds numbers, and oscillatory flows, as well as non-spherical particles, active particles, or particles with slip boundary conditions; all within a single unified framework. Furthermore, it provides direct access to all relevant dynamical properties of the fluid and the particles, allowing us to easily compute the particle contribution to the stress and the effective viscosity of the suspension. We have considered three simple cases in order to evaluate the accuracy and limitations of the model: a single sphere, two colliding spheres, and a rigid-bead chain. Comparison with analytical olutions, as well as Stokesian Dynamics simulations, shows good agreement in all cases. We will discuss the the sources of error inherent to the SPM, possible implementation issues, and how the SPM compares to alternative simulation methods for rheological studies.
[1] Hideki Kobayashi and Ryoichi Yamamoto, JCP 134, 06410 (2011).
[2] John J. Molina, Kotaro Otomura, Hayato Shiba, et al, submitted to J. Fluid Mech (2015).
- 2015/6/3 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Hiroyasu Tajima (Center for Emergent Matter Science (CEMS), RIKEN)
田島 裕康(理化学研究所 創発物性センター)
- Title
- Measurement-based Formulation of Quantum Heat Engine and Optimal Efficiency with Finite-Size Effect
量子測定理論に基づく量子熱機関の定式化と、有限多粒子熱機関の最適効率の導出
- Outline
- Today, theoretic analysis about such small-size heat engines is
achieving a splendid success. The statistical rederivation of
thermodynamical inequalities in macroscopic limit [1,2], thermodynamic
laws for processes with measurement and feedback [3,4], and
thermodynamic laws for the nano scale working bodies [5,6] are
particularly stimulative.
On the other hand, it is also true that there are many missing links
for constructing the thermodynamics of small-size systems. The above
researches formulate the quantum heat engine in various ways, and the
relationship among the formulations has not been sufficiently
discussed. There is little quantitative understanding of thermodynamic
laws in mesoscopic systems, i.e., the systems whose number of particle
is not so small but finite. There also has been little study done
concerning the finite-size heat baths.
Based on the above situation, we firstly establish a general formation
of the quantum heat engines on the quantum measurement theory. Our
formulation describes an arbitrary quantum heat engine that has some
equipment to assess the amount of the extracted work. With using our
formulation, we derive two trade-off relations that clarify a problem
of a widely-used formulation of quantum heat engine, in which the time
evolution of the internal system (heat engine and heat baths) is
formulated as a unitary transformation. The trade-off relations
clarify that we can hardly know the amount of the extracted work when
the time evolution of the internal system is close to unitary.
Second, we derive the optimal efficiency of quantum heat engines with
the finite-size heat baths, without assuming the existence of
quasi-static processes. We consider the work extraction from the pair
of hot and cold baths that are composed of n particles. Then, using
the strong large deviation theory, we asymptotically expand the
optimal efficiency up to the third order of Q_{n}/n, where Q_{n}
is the extracted heat from the hot bath. The first term is shown to be
Carnot efficiency, and the higher order terms are shown to be the
finite-size effects of the heat baths. We can construct the optimal
work extraction as an energy-preserving unitary time evolution among
the heat baths and the work storage. During the optimal work
extraction, the entropy gain of the work storage is so negligibly
small as compared with the energy gain of the work storage.
The details of the contents in this talk are in the article
arXiv:1504.06150, which is a collaboration with Prof. Masahito Hayashi
at Nagoya University.
[1]H. Tasaki, arXiv:cond-mat/0009244 (2000).
[2]P. Skrzypczyk, A. J. Short and P. Sandu, Nature Communications 5, 4185, (2014)
[3]T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 090602 (2010).
[4] L. Rio, J. Aberg, R. Renner, O. Dahlsten, and V. Vedral, Nature,474, 61, (2011).
[5]M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
[6]F. G. S. L. Brandao, M. Horodeck, N. H. Y. Ng, J. Oppenheim, and S. Wehner, PNAS, 112,3215(2015).
- 2015/5/27 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Masato Imami (Kyoto Univ.)
伊丹將人 (京都大学)
- Title
- Derivation of Stokes’ law without the hydrodynamic equations
ストークス則の流体方程式を前提にしない導出
- Outline
- When liquids and gases are out of equilibrium but still remain in local equi
librium, their macroscopic dynamical behavior is precisely described by the
hydrodynamic equations. Microscopic understanding of the hydrodynamic equa
tions for the case of dilute gases was established through the Boltzmann equ
ation, whereas it remains unclear for a general fluid.
In this presentation, we study the friction coefficient of a macroscopic sph
ere in a viscous fluid at low Reynolds number. According to Kirkwood’s form
ula [1], the friction coefficient is expressed in terms of the stress correl
ation on the surface of the sphere. Then, with the aid of large deviation th
eory, we relate the surface stress correlation to the stress correlation in
the bulk of the fluid, where the latter is characterized by the viscosity fr
om the Green–Kubo formula [2]. Namely, by combining Kirkwood’s formul
a and the Green–Kubo formula in large deviation theory, we derive Stok
es’ law [3] without explicitly employing the hydrodynamic equations [4].
[1] J. Kirkwood, J. Chem. Phys. 14, 180 (1946).
[2] M.S. Green, J. Chem. Phys. 22, 398 (1954).
[3] G.G. Stokes, Trans. Cambridge Philos. Soc. 9, 8 (1851).
[4] M. Itami and S. Sasa, arXiv:1505.01691.
- 2015/5/13 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Tetsuya Mitsudo (Kyoto Univ.)
光藤 哲也 (京都大学)
- Title
- Large deviations for frequencies in forest-fire models, diffusive elements and earthquake data
- Outline
- I would like to present two different studies concerning earthquakes.
1. Earthqukes increased after 2011 Tohoku earthquake in Japan. The most of increased earthquakes are explained by considering stress change, except for some regions where flow of water underground is related, and spreading of earthquakes is observed. We consider a diffusion model of earthquakes and apply the model to the earthquakes in the region. The diffusion model quantitatively succeeded in explaining the temporal change of the number of earthquakes in the real data.
2. We can find several characteristics of earthquakes in forest-fire models. For example, size-frequency distributions obey power-laws. In this simple model of earthquakes, we can calculate the large deviation function (LDF) for frequency for any system size when the ignition is allowed in a single cite at an edge. We found that the LDF for the frequency of size 1 is below the LDF of the homogeneous Poisson process, and a crossing in the largest eigenvalue may not occur.
- 2015/4/22 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Tatsuhiko Shirai (University of Tokyo)
白井 達彦 (東京大学大学院 理学系研究科)
- Title
- Novel symmetry-breaking phenomenon in a driven cavity system
駆動共振器系で現れる新奇な相転移現象について
- Outline
- Cooperative phenomena in the steady states in which the effects of the time-periodic driving external
field and the dissipation are balanced are studied. A cavity system in which quantized modes of photon fields are
interacting with materials is suitable for the study of this problem. We obtain the steady states by using
a quantum master equation.
We find a novel symmetry-breaking phenomenon which is interpreted as a synergistic phenomenon due to a quantum
interference effect of the driving external field and the strong interaction [1]. We discuss the mechanism in terms of
the Coherent Destruction of Tunneling (CDT) [2] originating from a quantum interference effect. In order to understand
this phenomenon quantitatively, we show the sufficient condition under which the driven steady state is described by
the Gibbs distribution of the Floquet state [3].
[1] T. Shirai, T. Mori, and S. Miyashita, J. Phys. B: At. Mol. Opt. Phys. 47, 025501(2014).
[2] F. Grossmann, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[3] T. Shirai, T. Mori, and S. Miyashita, Phys. Rev. E, 91, 030101(R) (2015).
- 2015/4/15 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Takeshi Kawasaki (Nagoya University)
川﨑 猛史 (名古屋大学)
- Title
- Rheology on soft-particle suspensions
やわらかい粒子系におけるレオロジー
- Outline
- Rheology of dense-particle suspensions is one of the central issues in condensed matter physics. In this seminar
we will show our recent results composed of topics, related to the sheared soft-particle suspensions.
The first topic is the comprehensive study of diverging viscosity below jamming transition and soft-particle rheology
above jamming [1]. Here we show that in the asymptotic behavior of the shear viscosity for the hard particle limit,
its power law divergence at the jamming transition represents `multiscaling' behavior. In addition, we propose a natural
extension of the standard granular rheology to account for softness effects, which differs from earlier empirical scaling forms.
The second topic is on shear thickening for soft-particle suspensions. We will show the role of inertia [2] and
friction in shear thickening.
[1] T. Kawasaki, D. Coslovich, A. Ikeda, and L. Berthier, Phys. Rev. E 91, 012203 (2015).
[2] T. Kawasaki, A. Ikeda, and L. Berthier, EPL 107, 28009 (2014).
- 2015/4/8 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Giacomo Marmorini (Yukawa Institute for Theoretical Physics, Kyoto University)
- Title
- Microscopic modeling of the quantum triangular antiferromagnet Ba3CoSb2O9
- Outline
- Frustrated antiferromagnets are a very rich class of physical systems, in which various new phases of matter are expected
to be realized. From a theoretical point of view, however, they present challenging difficulties and typically defy a full quantum
treatment. We employ a combination of dilute Bose gas theory and cluster mean-field theory to determine the ground-state phase
diagram of the prototypical spin-1/2 XXZ model on the triangular lattice and explain the magnetization process of Ba3CoSb2O9 [1,2].
Main results are as follows. i) A novel mechanism is found for which quantum fluctuations remove the classical degeneracy of ground
states of a frustrated spin system and stabilize a non-classical phase. ii) Agreement between the model calculation and the measured magnetization curves confirms Ba3CoSb2O9 as a geometrically almost perfect triangular-lattice magnetic insulator with small
easy-plane spin anisotropy as suggested by independent measurements (e.g. ESR). iii) The anomaly in the transverse field
magnetization of the same material can be explained by an additional first-order phase transition induced by the non-vanishing antiferromagnetic interlayer coupling, which is not present in the purely two-dimensional model; moreover, the model calculation
identifies this as a general feature of triangular-lattice easy-plane quantum antiferromagnets because it appears however small
the interlayer coupling is. If time allows we will discuss the possibility of getting new insights into quantum criticality from
further experimental study of Ba3CoSb2O9.
[1] D. Yamamoto, G. Marmorini and I. Danshita, Phys. Rev. Lett. 112, 127203 (2014).
[2] D. Yamamoto, G. Marmorini and I. Danshita, Phys. Rev. Lett. 114, 027201 (2015).