Academic Year 2016
- 2017/3/8 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Romain Mari
- Title
- Fragility of dense suspensions
- Abstract
The mechanical response of a suspension to an applied load is strongly dependent on its microstructure, that is, the statistics of the suspended particles' relative positions. In turn, the microstructure is itself strongly dependent on the history of the applied load. Hence, when the applied load changes rapidly compared to the relaxation time of the microstructure, there is a load/microstructure mismatch. This gives rise to very rich non-steady state behaviors, a well-known example being the complex response observed during a shear reversal. For this reason suspensions have sometimes been presented as a prototype example of ``fragile matter''. In this talk I will show simulation results exploring the fragility of dense suspensions in a systematic and quantitative manner. I will show how to use this feature, as well as self-organization, to achieve dramatic viscosity reduction in suspension flows.
- 2017/2/22 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Tomohiko Sano
- Title
- Slip, pinning, and snap-through of elastic ribbons
- Abstract
- Mechanics of elastic ribbons pushed vertically onto a frictional substrate is investigated numerically and analytically combined with experiments. We find a rich variety of morphologies, which are classified into three distinct types of states: pinned, partially slipped, and completely slipped states, depending on the vertical strain and static friction coefficient, when the bending elasticity dominates gravity. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb–Amontons friction law and find excellent quantitative agreement with simulations regarding the onset of slip events. We also discuss the effect of gravity in order to bridge the behaviors of stiff strips and those of flexible strings or ropes. Our study thus complements recent work on elastic rope coiling, making a significant step toward establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface. If time allows, we present recent progress on the exact solution of snap-through induced by sliding and its comparison with the corresponding experiments.
- 2017/2/13 (Mon):10:30-12:00, 13:30-15:00, 15:15-16:45
2017/2/14 (Tue):10:00-11:30, 13:00-14:30, 14:45-16:15
- @Seminar Room K206, Yukawa Institute
- Speaker
- Naomichi Hatano
- Title
- Non-Hermitian Quantum Mechanics of Open Systems
- Abstract
-
In the present lecture series, I will show how we can analyze open quantum systems in the context of non-Hermitian quantum mechanics. The open quantum system that I will consider is a one-body Hamiltonian that consists of a central scatterer on a compact support and a flat environment that extends to infinity.
Typical situations are a quantum with semi-infinite leads attached and a shell-model potential for a nuclied in an infinite space.
I will first show that such an open quantum system has eigenstates with complex eigenvalues. These states are historically called resonant states and anti-resonant states, but more precisely they are decaying and growing eigenstates. I will argue that the complexity of the eigenvalues do not contradict the Hermiticity of the Hamiltonian in the Hilbert space. I will also argue that, although these states diverge away from the central scatterer, the probability is conserved in an extended way.
I will stress that each of the resonant and anti-resonant states breaks the time-reversal symmetry despite that the original Schroedinger equation observes the time-reversal symmetry. Because of the symmetry of the equation, resonant and anti-resonant states always appear as a complex conjugate pair. Therefore, the system of solusions as a whole has the time-reversal symmetry.
I will next show how we can come up with an effective Hamiltonian of the whole infinite system on the compact support of the central scatterer. The effective Hamiltonian turns out to be non-Hermitian, reflecting the fact that it has complex eigenvalues. This approach lets us find a new complete set of the inifinite system that consists of states of point spectra including the resonant and anti-resonant states. I will stress that the complete set contains the pairs of resonant and anti-resonant states symmetrically.
I will finally argue that the problem of the arrow of time in quantum mechanics is solved by the newly found complete set. Why do we always see decay from an initial condition? I will show that the decaying eigenstates in the complete set excel in the time evolution for positive time, while the growing eigenstates do in that for negative time. The time thus works as an external magnetic field in the spontaneous symmetry breaking of the Ising model. Since we naturally ask what happnes after the initial condition, we always see decay in the time evolution, not growth.
References
G. Ordonez and N. Hatano, Self-generated breaking of time-reversal symmetry in open quantum systems, arXiv preprint arXiv:1610.01548
N. Hatano, G. Ordonez, Time-reversal symmetric resolution of unity without background integrals in open quantum systems, J. Math. Phys. 55 (2014) 122106 (40 pages)
N. Hatano, Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states, Fortschr. Phys. 61 (2013) 238--249.
K. Sasada, N. Hatano and G. Ordonez, Resonant Spectrum Analysis of the Conductance of an Open Quantum System and Three Types of Fano Parameter, J. Phys. Soc. Jpn. 80 (2011) 104707 (27 pages).
S. Klaiman and N. Hatano, Resonance theory for discrete models: Methodology and isolated resonances, J. Chem. Phys. 134 (2011) 154111 (9 pages).
N. Hatano and G. Ordonez, Resonant-state Expansion of the Green's Function of Open Quantum Systems, Int. J. Theor. Phys. 50 (2011) 1105--1115.
N. Hatano, Resonant states of open quantum systems, Prog. Theor. Phys. Suppl. 184 (2010) 497--515.
N. Hatano, T. Kawamoto and J. Feinberg, Probabilistic interpretation of resonant states, Pramana J. Phys. 73 (2009) 553-564.
N. Hatano, K. Sasada, H. Nakamura and T. Petrosky, Some Properties of the Resonant State in Quantum Mechanics and Its Computation, Prog. Theor. Phys. 119 (2008) 187-222.
K. Sasada and N. Hatano, Calculation of the Self-Energy of Open Quantum Systems, J. Phys. Soc. Jpn. 77 (2008) 025003 (2 pages).
- 2017/2/8 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Makoto Yamaguchi
- Title
- Markovian quantum master equation in the non-adiabatic regime
- Abstract
- The Markovian quantum master equation (QME) provides a key paradigm for the study of nonequilibrium statistical physics especially when the system Hamiltonian is time-independent. In recent years, however, quantum dissipative dynamics driven by a time-dependent external field is a research area of growing importance in various contexts, such as quantum annealing, quantum heat engines, and quantum thermodynamics. Nevertheless, no general way of rigorously constructing the Markovian QME is known for the time-dependent system Hamiltonian with the exception of the adiabatic regime [1].
In this talk, by introducing a temporal change time scale of the system Hamiltonian, we will discuss a general formulation of the Markovian QME to go well beyond the adiabatic regime. Then, we will show that in appropriate situations the framework is well justified even if the system Hamiltonian changes faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings may open up a new avenue for exploring the frontier in driven open quantum systems beyond the adiabatic regime [2].
[1] See, for example, A. Rivas and S.F. Huelga, Open Quantum Systems: An Introduction (Springer, Berlin, 2012).
[2] M. Yamaguchi, T. Yuge and T. Ogawa, Phys. Rev. E, in press; arXiv:1604.016301.
- 2017/2/8 (Wed) 14:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Tatsuro Yuge
- Title
- Perturbative approach to nonequilibrium steady state of quantum master equation
- Abstract
- The quantum master equation (QME), an equation of motion for an open quantum system, has been used to investigate nonoequilibrium phenomena in various fields. In the series of talks, we discuss extensions of applicability of the QME. This talk concerns an extension to relatively large systems in steady states, and the subsequent talk (by Dr. Yamaguchi) concerns an extension to non-adiabatic regime with time-dependent Hamiltonian.
In this talk, after reviewing some fundamental aspects of the QME, I focus on the nonequilibrium steady state (NESS) of the QME. In particular, I discuss a perturbative method of obtaining the NESS of the Redfield QME [1]. I show that this method is applicable to larger systems than those in direct method.
[1] T. Yuge and A. Sugita, JPSJ 84, 014001 (2015).
- 2017/1/31 (Tue) 16:00 - @Seminar Room K102, Yukawa Institute
- Speaker
- Michio Otsuki
- Title
- Effect of friction and avalanches on shear modulus of granular materials
- Abstract
-
Granular materials have rigidity above a critical density. This
transition, known as the jamming transition, is characterized by the
appearance of the storage modulus. It is well-known that frictionless
grains under infinitesimal strain exhibit a continuous transition of
the storage modulus. For finite strain, recent studies have revealed
that the storage modulus of frictionless grains decreases with
increasing strain as a result of slip avalanches. The present authors
have proposed a scaling law of the storage modulus to interpolate
between the states of small and large shear strain [1]. However,
little is known on the storage modulus of frictional grains.
In this seminar, we present our recent numerical results on the
storage modulus of frictional grains. The storage modulus for
sufficiently small strain exhibits a discontinuous transition, while
the transition becomes asymptotically continuous as the shear strain
increases due to the Coulomb criterion for the tangential friction
between grains. We propose a new scaling law to interpolate between
the continuous and the discontinuous transitions [2]. The frictional
grains also exhibit a nonlinear elastic behavior originated from the
slip avalanches under larger shear strain. We discuss the relation
between the nonlinearity and the size distribution of the avalanches.
[1]. M. Otsuki and H. Hayakawa, Phys. Rev. E 90, 042202 (2014).
[2].M. Otsuki and H. Hayakawa, arXiv:1612.00961
- 2017/1/25 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Kota Watanabe
- Title
- Non-adiabatic effects in quantum geometric pumping
- Abstract
-
近年、微小系における幾何学ポンプという現象が盛んに研究されている。通常、
マクロ系においては平均的にバイアスがなくてはカレントが存在しない。しかし
メゾスコピック系においては平均的にバイアスがなくてもカレントが存在しうる。
幾何学ポンプにおいてしばしば対象となる系は、量子ドットの左右に環境が取り
付けられたモデルである。このような系を解析するために有用なのは、環境の自
由度をトレースアウトしたマスター方程式を用いることである。温度や化学ポテ
ンシャルなどのパラメータを操作することにより、量子力学におけるベリー位相
に類似の量が現れ、それがポンプカレントと結びついている[1]。従来の研究で
はもっぱら断熱近似における解析が行われていた。これは解析が簡単になり、さ
らにポンプカレントとパラメータ空間上における曲率との対応が明確であるから
である。ただし、断熱近似はパラメータを無限小速度で操作することであるから、
このままではポンプのパワーというものはゼロになる。したがって実用上のポン
プを考える上ではどうしても非断熱的に考えざるをえない。
本発表では非断熱な場合に拡張した幾何学ポンプにおけるカレントおよびゆら
ぎの定理について述べる。手法は完全計数統計を反映した量子マスター方程式[2]
用いた。そしてその枠組みをスピンボソンモデルに適応し、カレントの平均を非
断熱的な場合において解析的表示を得た[3]。具体的にはポンプカレントの表式
を、パラメータ操作速度が小さいところで漸近展開を行うことで、断熱的な場合
との定量的な違いを得た。またゆらぎの定理を求め、その応用として揺動散逸定
理を始めとした各関係式を得た。その結果非断熱的効果が重要であることを示し
た[4]。また、これらの結果をスピンボソン系に対してMonte-Carlo simulation
を行い確認した。
[1] J. Ren, P. Hanggi and B. Li, Phys. Rev. Lett. 104, 170601 (2010).
[2] M. Esposito, U. Harbola and S. Mukamel, Rev. Mod. Phys. 81, 1665 (
2009).
[3] K. L. Watanabe and H. Hayakawa, Prog. Theor. Exp. Phys. 2014, 113A01
(2014).
[4] K. L. Watanabe and H. Hayakawa, arXiv:1701.02984 (2017).
- 2016/12/14 (Wed) 16:00 - @Seminar Room Y206, Yukawa Institute
- Speaker
- Ryosuke Yoshii
- Title
- Thermoelectric properties of SU(N) Kondo effect based on Fermi liquid theor
- Abstract
-
Since the first experimental observation of the Kondo effect in semiconducting quantum dot, the high experimental tunability of the mesoscopic system has revealed a lot of aspects for the Kondo effect. However the thermal transport in the presence of the Kondo effect is not yet well understood.
In this seminar, I will talk about the thermal transport in the presence of the Kondo effect in the basis of the Fermi liquid theory. I will show that the inner degrees of freedom in the quantum dot brings the qualitative difference into the thermal transport. I also show that the one of the Fermi liquid parameters appears in the thermal transport coefficients which does not appear in the case of the charge transport. This may bring the new insight to the Fermi liquid theory, which is powerful tool also applicable in the non-equilibrium situation.
- 2016/12/7 (Wed) 15:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Anael Lemaitre
- Title
- Anomalous phonon scattering and elastic correlations in amorphous solids
- Abstract
-
A major issue in materials science is why glasses present
low-temperature thermal and vibrational properties that sharply differ
from those of crystals. In particular, long-wavelength phonons are
considerably more damped in glasses, yet it remains unclear how
structural disorder at atomic scales affects such a macroscopic
phenomenon. A plausible explanation is that phonons are scattered by
local elastic heterogeneities that are essentially uncorrelated in
space, a scenario known as Rayleigh scattering, which predicts that
the damping of acoustic phonons scales with wavenumber k as k^{d+1}
(in dimension d). Here we demonstrate that phonon damping scales
instead as −k^{d+1} ln k, with this logarithmic enhancement
originating from long-range spatial correlations of elastic disorder
caused by similar stress correlations. Our work suggests that the
presence of long-range spatial correlations of local stress and
elasticity may well be the crucial feature that distinguishes
amorphous solids from crystals.
- 2016/11/30 (Wed) 16:00 - @Seminar Room YH206, Yukawa Institute
- Speaker
- Manabu Machida
- Title
- Linear Boltzmann transport and optical tomography
- Abstract
-
Optical tomography is an imaging modality which is similar to X-ray computed tomography but uses near-infrared light. The specific intensity of light in biological tissue obeys the radiative transport equation, which is a linear Boltzmann equation.
In this talk, I will explain how this Boltzmann equation emerges from light propagating in random media and how analytical solutions of the equation can be found. Optical tomography is formulated as an inverse problem for the radiative transport equation. Although this inverse problem usually relies on diffusion approximation, in this talk, I will obtain tomographic images by constructing the inverse Born series without diffusion approximation.
- 2016/11/14 (Mon) 13:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Tatsuhiko Ikeda
- Title
- Entanglement Pre-thermalization in an interaction quench between two harmonic oscillators
- Abstract
-
Foundation of quantum statistical mechanics has recently seen a resurgence of interest partly because ultracold atomic systems, which are almost perfectly isolated, serve as ideal testbeds (see e.g., Ref. [1] for an overview). Theoretical and experimental studies have revealed that a stationary state can appear within the unitary time evolution and it may or may not be thermal equilibrium depending, for example, on whether the Hamiltonian is chaotic or not.
Entanglement pre-thermalization (EP) is an approach to a non-thermal stationary state proposed in a situation where an isolated one-dimensional Bose gas is coherently split into two [2]. Each individual subsystem subsequently relaxes to a stationary state which can be well described by the canonical ensemble at an effective temperature, whereas the stationary state of the total system cannot be described by the canonical ensemble at any temperature due to quantum entanglement between the subsystems. However, due to technical difficulties in dealing with the one-dimensional Bose gas exactly, it has not been clarified what statistical-mechanical ensemble is suited to describe EP.
In this talk, following a brief review of the above-mentioned study, we present a study on EP using a toy model, which is an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP and find that a generalized Gibbs ensemble involving nonlocal conserved quantities describe EP exactly. We also discuss the effect of a perturbation which causes EP to relax into a true equilibrium state.
[1] L. D'Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, Adv. Phys. 65, 239 (2016).
[2] E. Kaminishi, T. Mori, T. N. Ikeda, and M. Ueda, Nature Physics 11, 1050 (2015).
- 2016/11/2 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- KIM Kang
- Title
-
Tuning Pairwise Potential Can Control the Fragility of Glass-Forming Liquids
- Abstract
-
The fragility, which characterizes the temperature dependence of the
transport properties, is one of the most important concepts of the
glass transition.
It is well known that anisotropic tetrahedral network-forming liquids
such as silica (SiO_2)
glasses exhibit the Arrhenius behavior, while isotropic short-ranged
potential liquids act as another type of glass-former exhibiting
super-Arrhenius temperature dependence.
Here, it is demonstrated that the fragility can be controlled over a
wide range by tuning the potential in a single simulation model.
Our simulations are based on a silica glass former model originally
proposed by Coslovich and Pastore (CP). This CP model uses the
short-ranged and attractive pairwise potential between Si and O in order
to mimic the anisotropic tetrahedral network structure.
We reveal that the reduction of the potential depth, eventually
transforming into the isotropic structure with the purely repulsive
soft-sphere potential, seamlessly changes the temperature dependence
of the relaxation time from Arrhenius to super-Arrhenius.
[1] M. Ozawa, K. Kim, and K. Miyazaki, J. Stat. Mech. 074002 (2016).
- 2016/10/19 (Wed) 16:00 - @Seminar Room K102, Yukawa Institute
- Speaker
- Tomotaka Kuwahara
- Title
- Fundamental inequalities in quantum many-body systems
- Abstract
- In this talk, I discuss the non-degenerate gapped quantum states in general Hamiltonians.
In understanding the ground states in many-body systems, we usually focus on the fact that the states
occupy only a small corner of the total Hilbert space. The information on the restrictions serves for optimizing
approximated numerical and/or analytical schemes, such as mean-field approximation and the density matrix
renormalization-group method. Currently, rigorous constraints have been hardly known in many-body
systems beyond one dimension. On the ground states’ structure, I expose a new universal constraint “local reversibility”
which complements the insufficiency of the existing ones, namely the exponential clustering and the area law of the
entanglement entropy. It rigorously holds for all quantum many-body ground states, including higher dimensional systems or long-range interacting systems.
From the results, we prove that the macroscopic superposition cannot exist in the gapped ground state in terms of the Fisher information.
- 2016/8/3 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Ryota Shinagawa (Tohoku Univ.)
- Title
- Enhancement of rotational diffusion coefficient of rotational molecular motors
-
Abstract
- In a periodic potential the diffusion of Brownian particles is enhanced by applying an external force. The diffusion is larger than free diffusion (without the periodic potential). The dependence of diffusion coefficient $D$ on external force $F$ has a peak, whose position corresponds to the maximum slope of the periodic potential [1]. It means that if we do not know the potential we can obtain information on the potential from the force dependence of diffusion coefficient $D(F)$.
Recently this theory was applied to a rotational molecular motor F$_1$-ATPase (F$_1$). F$_1$ consists of a rotor and a stator which surrounds the rotor. The rotor is captured by the interaction potential between the rotor and the stator. By using the chemical energy of adenosine triphosphate (ATP)-hydrolysis the interaction potential between the rotor and the stator is stochastically switched, which results in the rotation of the rotor by 120 degrees. This potential was estimated by measuring the torque N dependence of rotational diffusion coefficient of the rotor of F$_1$ without ATP [2].
Our study aims to make it possible to get the information about not only interaction potential but also transition-rate of F$_1$ by measuring the position of the peak of $D(N)$ in the presence of ATP. We constructed a model by modifying the previous model [3]. We numerically solved the Fokker-Planck equation to obtain $D$. The result showed that $D(N)$ had a peak even in the presence of ATP [4]. We found that at high ATP concentration we can get the information about the interaction potential as in the previous study [2]. Furthermore at the low ATP condition the position of the peak depends on the ATP concentration and it provides us with the insight into transition-rate.
[1] P. Reimann {\it et al.}, Phys. Rev. Lett. {\bf 87}, 010602 (2001).
[2] R. Hayashi {\it et al.}, Phys. Rev. Lett. {\bf 114}, 248101 (2015).
[3] K. Kawaguchi {\it et al.}, Biophys. J. {\bf 106}, 2450 (2014).
[4] R. Shinagawa and K. Sasaki, J. Phys. Soc. Jpn. {\bf 85}, 064004 (2016).
- 2016/7/26 (Tue) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Raphael Blumenfeld (Imperial College, London)
- Title
- Progress in statistical mechanics of a-thermal particulate systems
- Abstract
- Sam Edwards’s formulation of statistical mechanics for granular media not only made science of particulates more rigorous but also opened a new branch of soft matter physics. In this presentation I review briefly the Edwards formalism, which has been extended to cellular and porous materials, and some of its assumptions. A certain problem with the original formalism is discussed and a new way to overcome it is proposed. Finally, a derivation of an equation of state with the new formalism is presented, which relates the volume, the boundary stress and measures of the structural and stress fluctuations.
- 2016/7/6 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Hisao Hayakawa (YITP)
- Title
- Kinetic theory of discontinuous shear thickening
- Abstract
- A simple kinetic theory to exhibit a discontinuous shear thickening
(DST) is proposed. The model includes the collision integral and the
friction from environment as well as a thermostat term characterized
by $T_{\rm ex}$. The viscosity of this model is proportional to which
is consistent with the observation by Kawasaki et al. (EPL {\bf 107},
28009 (2014))
for large shear rate $\dot\gamma$, while it is Newtonian for low
$\dot\gamma$. The DST emerges as a suddle-node bifurcation arising
from the connection between Newtonian branch and the branch at $T_{\rm
ex}=0$. The emergence of the DST is enhanced for lower density and
lower nonzero $T_{\rm ex}$. The proposed mechanism is new, because the
DST is unrelated to neither mutual friction of grains, the
order-disorder transition, boundary effects nor hydro-clustering
mechanism.
This talk is based on the collaboration with Satoshi Takada, and the
related paper is going to be submitted before the seminar.[1]
[1] H. Hayakawa and S. Takada, in preparation.
- 2016/6/29 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Ryohei Seto (Okinawa Institute of Science and Technology Graduate University)
- Title
- Discontinuous Shear Thickening Fluid in a Wide-Gap Couette Cell
- Abstract
- Recent particle-based simulations have demonstrated the capacity to accurately reproduce shear thickening of dense suspensions observed in experiments [1]. These simulations provide insight regarding the influence of particle-scale mechanisms on the bulk rheology: a stress-induced transition from a reasonably viscous flow of lubricated near-contacting particles to a highly viscous flow of a frictionally contacting network of particles can cause very steep or even discontinuous dependence of the viscosity on the shear rate. Next important step is to construct a kind of kinetic model which is compatible with the simulation conditions. It would be very challenging to develop models describing such non-equilibrium steady states involving non-conservative interparticle interactions. The other important step is to bring insights from local bulk rheology to macroscopic flow. The particle simulations are restricted to simple shear flows because of use of Lees-Edwards periodic boundary conditions for small system sizes (several thousand particles). Such conditions may exclude possible macroscopic flow behavior, including migration or instabilities such as shear banding. Actually, S-shaped rheology curves were observed in particle simulation[2], but never in real experiments. Recently, shear banding and migration of shear thickening suspensions in wide gap Couette cells were examined by using magnetic resonance imaging [3, 4]. Shear thickening occurs at the rotational rate where the migration and shear banding are observed. I will introduce suspension rheology in the context of physics and discuss our recent challenge to extend particle-based simulation to capture such non-uniform shear thickening behaviors.
[1] R. Mari, R. Seto, J. F. Morris, and M. M. Denn. Discontinuous shear thickening in brownian suspensions by dynamic simulation. Proc. Natl. Acad. Sci. USA, 112(50):15326–15330, 2015.
[2] R.Mari,R.Seto,J.F.Morris,andM.M.Denn.Nonmonotonicflowcurvesofshearthickening suspensions. Phys. Rev. E, 91:052302, May 2015.
[3] H. de Cagny, A. Fall, M. M. Denn, and D. Bonn. Local rheology of suspensions and dry granular materials. J. Rheol., 59(4):957–969, 2015.
[4] A.Fall,F.Bertrand,D.Hautemayou,C.Mezière,P.Moucheront,A.Lemaître,andG.Ovarlez. Macroscopic discontinuous shear thickening versus local shear jamming in cornstarch. Phys. Rev. Lett., 114:098301, Mar 2015.
- 2016/6/22 (Wed) 13:30 - @Seminar Room K202, Yukawa Institute
- Speaker
- Koshiro Suzuki, Canon Inc.
- Title
- Theory for Divergent Viscosity in non-Brownian suspensions
- Abstract
- Jamming transition is an athermal phase transition of amorphous
solids, which is characterized by the divergence of viscosity. This
phenomenon is universely observed in disordered materials such as
colloidal suspensions, emulsions, foams, granular materials, etc. In
ref.[1], we have proposed a theoretical approach to this phenomenon in
sheared granular materials, and have shown that the analytic formula
for the viscosity derived from this theory agrees well with the result
of the MD simulation up to the jamming density.
Our theory is based on an explicit approximate expression for the
steady-state nonequilibrium distribution function for weakly sheared
cases. The framework of the theory is generic and hence it is expected
to be applicable to other materials which exhibit jamming. In the
present talk, we apply the theory to non-Brownian suspensions and show
how the divergence of the viscosity is derived in this framework. We
will compare the theoretical results with MD simulations and also
compare with the preceding related works.
[1] K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 115, 098001 (2015).
- 2016/6/8 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Daisuke Sato (Earthquake Research Institute, The University of Tokyo)
- Title
- Normal heat conduction in one dimensional momentum-conserving systems
- Abstract
- The transportation phenomena have been the soil of the discoveries of the fundamental nonequilibrium theorems e.g. the linear response theory and the fluctuation theorem. On the other hand, the foundation of themselves is still under the discussion[1]. Now we know the significance of the dimensionality. The transportation coefficients grow with the power of the system-sizes in low dimensional systems (anomalous transport)[1]. It means the divergence of the coefficients in the thermodynamic limit and yields a counterintuitive conclusion that hydrodynamic descriptions cannot exist. This phenomenon is already observed in the heat conduction (anomalous heat conduction) and even under the discussion of its applications[2]. The topic of this talk is on the low dimensional systems of heat conduction.
In the colloquium, we report the possible theoretical foundation of the exception of it, the recovery of the normal heat conduction (the intensive property of the coefficient)[3]. We firstly construct the examples of the subclasses of the exception (Dissociation-Induced/ Pressure-Induced) by MD and then provide them with the quantitative explanations. The former corresponds to the mechanism already pointed out in [4] and we described it by the rate theory. The analysis of the latter is based on the renormalization group of the fluctuating hydrodynamics (though it has shown the theoretical basis of the anomalous transport[1]) and predicts the following. The compressibility yields another nontrivial fixed point from that corresponding to the anomalous transport. This new fixed point shows the theoretical basis of the normal heat conduction in low dimensional systems. In this sense, the compressibility is a relevant parameter of the fluctuating hydrodynamics. Two equal mechanisms can be just compared to those of the glass transition[5].
In the presentation, we briefly overview the previous works and discuss about ours[3]. We also explain about the renormalization group method[6] as possible as we can.
[1] S. Lepri, R. Livi, and A. Politi, Physics Reports 377, 1 (2003).
[2] C.-W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Physical review letters 101, 075903 (2008).
[3] Sato, Dye SK. arXiv preprint arXiv:1511.02585 (2015) (To be published in PRE).
[4] O. Gendelman and A. Savin, EPL (Europhysics Letters) 106, 34004 (2014).
[5] K Miyazaki, Bussei Kenkyu, 88(5): 621-720 (2007).
[6] D. Forster, D. R. Nelson, and M. J. Stephen, Physical Review A 16, 732 (1977).
- 2016/6/1 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Giacomo Marmorini (Yukawa Institute for Theoretical Physics, Kyoto University)
- Title
- Correlations of Tonks-Girardeau anyons in a harmonic trap
- Abstract
- After a general introduction of generalized statistics with a focus on one-dimensional systems and some proposed cold-atom realizations, we study in detail the one-body reduced density matrix of a system of N impenetrable (delta-interacting) anyons trapped in a harmonic potential in one dimension. To this purpose we extend two methods previously applied to related problems, namely the reformulation in terms of the determinant of a Hankel matrix and the replica method. While the former is the basis for highly accurate numerical results, the latter has the advantage of providing an asymptotic expansion in analytic form. We show that the first few terms of such expansion are sufficient to reproduce the numerical results to an excellent precision even for relatively small N, thus demonstrating the efficiency of the replica method.
- 2016/5/25 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Andres Santos (Departamento de Fisica, Universidad de Extremadura)
- Title
- Hydrodynamics for granular flow at low density: Navier-Stokes and Burnett
constitutive equations
- Abstract
- Dilute granular gases can be successfully described at a microscopic level by
the Boltzmann kinetic equation as applied to simple models of particles
colliding inelastically. In principle, a hydrodynamic-level description can
subsequently be derived in the regime of weak field gradients by means of the
celebrated Chapman-Enskog method. So far, the most frequently used granular
model has been the inelastic smooth hard-sphere model (ISHSM). In this talk, two
main classes of models will be considered: the inelastic and rough hard-sphere
model (IRHSM) and the inelastic Maxwell model (IMM). The former considers hard
spheres with translational and angular velocities whose binary collisions are
characterized by constant coefficients of normal and tangential restitution. In
the simpler IMM, the collision rule is the same as in the ISHSM, and hence the
rotational degrees of freedom are irrelevant, but the collision rate is assumed
to be independent of the relative velocity of the colliding pair (hence the term
"Maxwell"). In the first part of the talk, the Navier-Stokes constitutive
equations for the three-dimensional IRHSM will be presented, the first Sonine
approximation being used to obtain explicit expressions of the transport
coefficients as nonlinear functions of both coefficients of restitution and the
moment of inertia. Known results for the ISHSM and for the conservative case of
perfectly elastic and rough spheres are recovered in the appropriate limits. In
the second part, the hydrodynamic Burnett equations and the associated transport
coefficients are exactly evaluated for the IMM in any dimensionality. Some
transport coefficients that are related in a simple way in the elastic limit
become decoupled in the inelastic case. As a byproduct, existing results in the
literature for three-dimensional elastic systems are recovered and a
generalization to any dimension of the system is given. The structure of the IMM
results is used to estimate the Burnett coefficients for the ISHSM.
- 2016/5/18 (Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- Purusattam Ray (The Institute of Mathematical Sciences, CIT Campus, Taramani)
- Title
- Shock Propagation in Granular Systems
- Abstract
- We present the study of the response of a granular system at rest to an
instantaneous input of energy in a localized region. Scaling arguments are
presented that show that, in d dimensions, the radius of the disturbed zone
increases with time t as a power law with power alpha = 1/(1+d), irrespective of
the value of the coefficient of restitution. We support our arguments with an
exact calculation in one dimension and even-driven molecular dynamics
simulations of hard-spherical particles in two and three dimensions. We compare
our results with those obtained from experiments and extend our arguments to
continuously driven granular gas.
- 2016/5/9 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Shunsuke Yabunaka (Yukawa Institute for Theoretical Physics, Kyoto University)
- Title
- Hydrodynamics in bridging and aggregation of two colloidal
particles in a near-critical binary mixture
- Abstract
- We investigate bridging and aggregation of two colloidal
particles in a near-critical binary mixture when the fluid far from the
particles is outside the coexistence (CX) curve and is rich in the
component disfavored by the colloid surfaces. In such situations, the
adsorption-induced interaction is enhanced, leading to bridging and
aggregation of the particles. We realize bridging firstly by changing
the temperature with a fixed interparticle separation and secondly by
letting the two particles aggregate. The interparticle attractive force
dramatically increases upon bridging. The dynamics is governed by
hydrodynamic flow around the colloid surfaces. In aggregation, the
adsorption layers move with the particles and squeezing occurs at narrow
separation. We take into account the renormalization effect due to the
critical fluctuations using the recent local functional theory[J. Chem.
Phys. 136, 114704 (2012)].
- 2016/4/25 (Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Kuniyasu Saitoh (WPI Advanced Institute for Materials Research (AIMR), Tohoku University)
- Title
- Anomalous energy cascades in dense granular materials yielding under shear
- Abstract
- Granular materials are ubiquitous in nature and a better understanding of their flow properties is crucial to industry and science, where the granular rheology strongly depends on the fraction (or density) of the constituents, e.g. if the fraction is small, Bagnold’s scaling (for shear stress proportional to the square of shear rate) predicted by kinetic theory well describes the flow behavior, while we observe a finite yield stress once the fraction exceeds a critical value. In such yielding states of granular materials (or “critical state” in the literature on civil engineering), the kinetic theory fails to explain the rate-independent contact contribution to the shear stress, where many phenomenological models (e.g. the mu-I rheology, order-parameter descriptions, non-local model for slow flows, etc.) have been proposed without the microscopic insight into yielding granular materials.
In this study, we investigate microscopic structures of dense granular particles under simple shear deformations and connect our findings to the macroscopic flow behavior. Employing two-dimensional molecular dynamics (MD) simulations, we observe that non-affine velocities, which represent complicated rearrangements of granular particles around the mean velocity field, exhibit turbulent-like structures, e.g. unusual statistics and strong correlations of non-affine velocities. In addition, we find that the energy spectrum (defined by non-affine velocities and associated with granular temperature rather than the total kinetic energy) shows the clear power-law decay (as usual turbulence does) if the system is yielding under quasi-static deformations. To explain the anomalous energy cascades observed in our MD simulations, we adopt Savage’s continuum theory for dense granular materials, where we derive a theoretical expression of the energy spectrum from hydrodynamic modes of non-affine velocity fields and confirm a good agreement with our results of MD simulations in a wide range of length scales [1].
We also plan to mention more detailed analyses of the turbulent-like structures, the impact of microscopic frictions between the particles in contacts, and the anisotropic decay of the energy spectrum.
[1] Kuniyasu Saitoh and Hideyuki Mizuno, “Anomalous energy cascades in dense granular materials yielding under simple shear deformations”, Soft Matter 12 (2016) 1360. Communication.
- 2016/4/20 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Yuliang Jin (Cybermedia Center, Osaka University)
- Title
- Numerical detection of the Gardner transition in hard sphere glass formers under compression and shear
- Abstract
- Low-temperature crystals can be modeled as harmonic vibrations, the phonons, around a perfect lattice. The resulting Debye theory perfectly predicts thermodynamic and transport properties. Low-temperature glasses instead display all kind of anomalies with respect to this description: anomalous specific heat and thermal conductivity; activated slow dynamics across barriers inside the glass; an abundance of soft vibration modes with respect to the Debye law, the so-called Boson Peak; marginal stability of mechanical excitations; a plastic and irreversible response to arbitrarily small strain amplitudes. All these observations can be rationalized as the remanent of a novel phase transition, the Gardner transition, predicted by the mean field theory of glasses. The Gardner transition distinguishes between two types of amorphous solids: the simple mechanically stable glass and the marginally-stable glass. Here we explore numerical methods to detect the Gardner transition in several model glass formers [1,2]. We show evidence for the existence of the Gardner transition in ultrastable glasses under external perturbations: compression and shear. We find that the transition is associated to (i) the significant growth of time and length scales, (ii) the spatially heterogeneous organization of cages that confine particles’ vibrations, (iii) the nontrivial change of the probability distribution function of caging order parameters, and (iv) the emergence of protocol-dependence shear modulus. We further discuss the connection between our results and experiments in low-temperature glasses.
[1] L. Berthier, P. Charbonneau, Y. Jin, G. Parisi, B. Seoane, and F. Zamponi, arXiv:1511.04201 (2015).
[2] P. Charbonneau, Y. Jin, G. Parisi, C. Rainone, B. Seoane, and F. Zamponi, Phys. Rev. E 92, 012316 (2015).
- 2016/4/13 (Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Andreas Dechant (Kyoto University)
- Title
- Power-law statistics, equipartition violations and scaling in
confined cold atoms
- Abstract
- Laser cooling of atoms and ions is nowadays a common
technique in many laboratories and has enabled a range of
groundbreaking experiments in quantum mechanics and quantum optics.
But laser cooled atoms themselves are also worth considering from the
point of view of statistical mechanics, as they constitute a very
well-controlled system coupled to the tunable nonequilibrium “heat
bath” of the laser field. We consider the particular case of Sisyphus
cooling, where the interaction between the atoms and the light field
leads to an effective, highly nonlinear friction force, resulting in a
power-law momentum distribution and Levy-walk like superdiffusive
spreading. By contrast, spatially confining the motion of the atoms
allows them to reach a steady state distribution, which nevertheless
retains the power-law high-energy tails. We examine the properties of
this steady state in three analytically tractable limits and find a
highly non-trivial structure in phase-space. In particular, the
equipartition theorem breaks down and kinetic and potential energy may
differ dramatically. Finally, we discuss the limits of the steady
state description and the scaling properties of the time-dependent
solution.