2013年度
- 2014/03/05(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 村下 湧音 (東大理学系研究科物理学専攻)
- Title
- ルベーグ分解に基づく非平衡等式
- Outline
- 近年,平衡から遠く離れた非平衡過程を定量的に記述する揺らぎの定理に関心が持たれている.
これらの等式は系にフィードバック制御を行う場合にも拡張されている.
しかし,非平衡過程に自由膨張が含まれる場合には積分型の揺らぎの定理が適応できないことが知られている[1].
特に,フィードバック制御の際に射影測定を行った場合,系の状態が位相空間内の有限領域に制限される.
そのため,理想的なフィードバックを行わない限りフィードバック過程に自由膨張が含まれ,積分型揺らぎの定理を適用できない.
これらの基本的な過程にも積分型揺らぎの定理を拡張することが望ましい.
本発表では,これらの過程にも適応できる積分型揺らぎの定理を導く[2].
自由膨張に積分型揺らぎの定理が適応できないことの要因は,時間反転過程を考える際に,
対応する順経路を持たない逆経路が存在することである.
Lebesgue分解定理を用いることで,この問題となる部分を確率測度の特異部分として,エントロピー生成が定義できる部分から分離し,
新たな積分揺らぎの定理を導く.
さらに,導かれた等式からJensenの不等式により導出される不等式は,
従来の情報熱力学第二法則よりもエントロピー生成の下限に強い制約を与える.
また,新たな非平衡等式に対する数値的検証の結果も紹介する.
[1] Christopher Jarzynski, “Reply to comments by D.H.E. Gross,” arXiv:cond-mat/0509344 (2005).
[2] Yuto Murashita, Funo Ken, and Masahito Ueda, “Nonequilibrium Equalities Derived from Lebesgue's Decomposition,” arXiv:1401.4494 (2014).
- 2014/02/26(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 齊藤 国靖 (University of Twente, the Netherlands)
- Title
- Shear banding in dense granular flow: A new law for the friction coefficient
- Outline
- Dense granular flow is ubiquitous in science and technology, where many studies focus on the constitutive relation in “dry
frictional”granular materials. One of successful methods for describing the rheology is like Coulomb’s law of friction, i.e.
the shear stress is proportional to the normal stress, and the friction coefficient found in experiments is dependent only on
the so-called inertial number. In this study, we simulate dense granular flows in a cyclic shear geometry with split bottom by
discrete element methods [1]. Though the previous studies have concluded the friction coefficient is (almost) independent of
particle's stiffness, we find that it decreases with the stiffness if the particles are moderately rigid. For a given stiffness,
we also study its dependence on the gravity and describe the friction coefficient in terms of a dimensionless number consists of
the stiffness and gravity, where the friction coefficient is given by the power law of the dimensionless number. We also
investigate how the friction force and cohesive force between particles alter the shear banding in dense granular flow [2].
[1] “Does gravity have an effect on the slow shear rheology of granular matter?”,
A. Singh, V. Magnanimo, K. Saitoh, and S. Luding, submitted to Phys. Rev. E
[2] “Effect of cohesion on shear banding in quasi-static granular material”,
A. Singh, V. Magnanimo, K. Saitoh, and S. Luding, submitted to Phys. Rev. E
- 2014/02/24(Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 瀬戸 亮平 (ニューヨーク市立大学シティカレッジ)
- Title
- シアーシックニング:サスペンションレオロジーと摩擦
- Outline
- Dense particle suspensions often exhibit shear thickening: suspension becomes more viscous when sheared faster.
The dependence on shear rate is even discontinuous in some cases.
Our work explains the actual mechanism of shear thickening [1].
Suspension rheology has historically been studied from a fluid mechanics perspective,
and the emphasis has been on a description based on hydrodynamic interactions.
Because of the universality of the phenomenon,
researchers have focused on simple models to reproduce shear thickening:
rigid spheres immersed in a Newtonian fluid, interacting through hydrodynamics (including Brownian forces)
and sometimes an additional soft potential, e.g., of DLVO type.
The key point is that the particles are treated as mere boundary conditions for the Stokes equations
describing the fluid phase, and they never directly generate forces through contacts.
This is self-consistently justified by the fact that the Stokes flow
between two rigid surfaces leads to the singular lubrication force, preventing two particles from colliding.
While these fluid-mechanics based models do predict shear thickening,
the shear-rate dependence is much more moderate than observed experimentally.
The discontinuous dependence has remained a mystery.
We have reconsidered the assumptions used in previous simulation models and introduced a new working hypothesis:
the lubrication force remains finite at contact.
As long as it is finite, the possibility of contact cannot be excluded,
which means that we need to introduce a proper contact force model, i.e., friction.
Our model also assumes a repulsive force (or a threshold force to activate frictional contacts),
which introduces a shear rate dependence.
Frictional contacts restrict the smooth reorganization of particles to adapt to the shear strain.
Once created, local disturbance propagates through a pileup effect;
frictional contacts tend to become chains. Due to friction,
these chains can temporary behave as rigid rods with compatible stresses.
Upon increase of the shear rate (and shear stress), creating frictional contacts becomes easier,
leading to more and longer chains. If the suspension is not concentrated enough,
the viscosity continuously increases as chains grow.
But, if the suspension is sufficiently concentrated, there is a point
at which such rigid entities span the entire space and the system becomes a solid,
i.e., (a kind of) jammed phase.
At this point, one observes a discontinuity in the shear-rate dependence of viscosity.
[1] R. Seto, R. Mari, J. F. Morris, and M. M. Denn. Discontinuous shear thickening of frictional hard-sphere suspensions.
Phys. Rev. Lett., 111:218301, 2013. doi: 10.1103/PhysRevLett.111. 218301.
- 2014/02/19-20 @Seminar Room K206, Yukawa Institute
- Speaker
- 出口哲生 (お茶の水女子大学 大学院人間文化創成科学研究科)
- Title
- 集中講義:可積分量子多体系の非平衡ダイナミクスと統計力学の基礎
- Outline
- 19日:13:00-14:30, 14:40-16:10, 16:20-18:00
20日:9:00-10:30, 10:40-12:00, 13:00-14:30, 14:40-16:10, 16:20-17:00
最近、孤立した量子多体系のダイナミクスが活発に研究されている。
例えば、レーザーで閉じ込められた冷却原子系において、系の物理量が緩和する過程が実験で観察された。
理論的にも、相互作用クエンチなど、外場変数を急変化させた後に生じる量子多体系のダイナミクスに関心が集まっている。
量子系におけるクエンチの問題は、70年代はじめにMcCoy 達によって可解系を用いて最初に議論された。
しかし、注目を集めるようになったのは今世紀以降で、比較的最近である。
これは量子クエンチが実験で調べられるようになったためであろう。
理論的研究方法として、量子多体系の時間発展を長時間にわたって数値的に追跡することは、一般には困難である。
しかし可積分系を用いると、特に初期状態によっては、その後の系の時間発展を非常に長時間にわたって厳密に追跡することができる。
量子多体系のダイナミクスの特徴を明らかにする上で、可積分量子系は重要な例を与える可能性がある。
孤立量子系のダイナミクスは、最近、量子統計力学の基礎の視点からも興味を持たれている。
量子多体系の純粋状態を任意に与えると、ほとんどの場合は平衡状態に非常に近いことが明らかにされた(Cf. H. Tasaki, PRL(1998))。
これを典型性(typicality) とよぶ。
そして、与えられた純粋状態のユニタリ―な時間発展の中で、局所演算子の期待値がある平衡状態のアンサンブル平均値に収束する、
と予想されている。系のエントロピーは変化しないので、従来の意味での緩和とよぶのはあまり適当ではなく、
最近では、平衡化 (equilibration) あるいはもし初期状態依存性がない場合には熱化(thermalization) とよばれる。
しかし、見る限りではあたかも緩和するかのような時間発展が観察される。
このことを、例えば可積分量子系を用いて確認することができる[1]。
非可積分な孤立量子多体系の時間発展では、局所物理量の期待値は、漸近的にミクロカノニカル分布の値に収束すると予想され、
多くの例で確かめられている[2,3]。
一方、可積分量子系にはハミルトニアンと交換する多数の保存量演算子が存在する。
このため、可積分系の時間発展は非可積分系の場合とは異なり、
一般化されたギブス分布に収束することがRigol 達によって予想された[2]。
これは独立な保存量の数だけ拡張された温度変数が対応するような分布であり、これらの一般化熱力学変数の値は、
初期状態における保存量演算子の期待値で決定される。
この予想は証明されてはいないが、いくつかの重要な例で確認されている[4]。
歴史的には70年代初頭に、線形応答における保存量の効果が議論されており(P. Mazur (1969), M. Suzuki (1971))、
これらの結果とも深く関係している[4]。
さらに、可積分量子系のダイナミクスにおいて、ある物理量の時間やサイズ依存性に関して冪的な振る舞いが見られるなど、
興味深い観察が導かれている。一方、物理量の振幅が時間的に冪的に減衰する実験の例も報告された。
このため、可積分系の非平衡ダイナミクスにおける様々な特徴を明らかにすることは、実験の結果を理解する上でも興味深い。
また、孤立量子多体系のダイナミクスの特徴を明らかにすることは、
例えば外場の変化に対する超短時間での系の挙動を解析することに相当し、
さらに、量子多体系を制御する方法に発展する可能性もある。
このため、応用面からの興味も将来的には十分考えられる。
2日間の集中講義では、最初に上記のような研究状況のおおよその説明を行った後に、
可積分量子系の最も重要な研究方法の一つとして、代数的べーテ仮設法の入門を分かり易く説明する[5]。
そして、形状因子やスカラー積のスラブノフの公式[6]、
任意の局所演算子を生成消滅演算子を用いて代数的に表す逆散乱問題公式[7]など、
局所演算子の期待値を調べるのに役立つ主要な定理を説明する。
このあたりの事柄に関してあまり分かり易い文献がないので、それを補おうことを試みたい。
そして、1次元ボース気体や1次元ハイゼンベルグ模型などを用いて最近分かった厳密な結果などを紹介する。
参考文献:
[1] J. Sato, R. Kanamoto, E. Kaminishi, and T. Deguchi, Exact Relaxation Dynamics of a Localized Many-Body State in the 1D Bose Gas, Phys. Rev. Lett. Vol. 108, 110401 (2012).
[2] M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. Vol. 98, 050405 (2007).
[3] M. Rigol, V. Dunjko, and M. Olshanii, Nature Vol. 452, 854 (2008).
[4] A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Rev. Mod. Phys. Vol. 83, 863 (2011).
[5] 出口 哲生、1次元量子系の厳密解とベーテ仮説の数理物理、物性研究 Vol. 74-3 (2000-6) pp. 255-319.
[6] V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, (Cambridge Univ. Press, Cambridge, 1993).
[7] N. Kitanin, J. M. Maillet and V. Terras, Form factors of the XXZ Heisenberg spin-1/2 finite chain, Nucl. Phys. B Vol. 554 [FS], 647 (1999).
- 2014/02/05(Wed) 17:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 江藤 幹雄 (慶應義塾大学 理工学部 物理学科)
- Title
- 半導体二重量子ドットにおける光学フォノンレーザー
- Outline
- 半導体基板に作製した二重量子ドットの非平衡電気伝導において、光学フォノンレーザー、およびアンチバンチングの生成を提案する。
フォノンを閉じ込めるキャビティは不要である。
まず、二重量子ドット中の電子はフォノンの2つのモードのみと結合すること、そのモード自体がキャビティの役割をすることを示す。
電子のポンピングは、有限バイアス下の電流によって実現される。
量子ドットとリード間のトンネル率がフォノンの崩壊率より大きいときにフォノンレーザーが発振すること、
逆の場合はフォノンのアンチバンチングが生成されることを、数値計算と解析解の両者によって導出する。
カーボンナノチューブ上に作製した2重量子ドットでは、電子格子相互作用が強過ぎるため、
フランク・コンドン効果によってレーザーやアンチバンチングの生成が困難となる。
この理論はNEMS(ナノメートルスケールの機械構造を持つデバイス)への応用等が期待される。
[参考文献]
[1] R. Okuyama, M. Eto, and T. Brandes, J. Phys. Soc. Jpn. 82, 013704 (2013), selected as "Editors Choice."
[2] R. Okuyama, M. Eto, and T. Brandes, New J. Phys. 15, 083032 (2013).
- 2014/01/15(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 下出敦夫 (京都大学大学院理学研究科)
- Title
- Heat Responses and Field Theory in a Curved Spacetime
- Outline
- Heat transport is a traditional issue,
but recently has attracted renewed interests in the context of the anomalous Hall effect
and topological superconductivity.
Although we expect the charge-heat analogy,
we do not know heat responses compared to electromagnetic responses.
According to the electromagnetism, scalar and vector potentials are coupled to the charge and charge current densities,
respectively. Then what are gauge potentials coupled to the heat and heat current densities?
Luttinger gave the answer to the first question, and introduced a gravitational potential to formulate heat transport [1].
In this talk, we give the answer to the second question.
We reveal that the Lorentz-temporal component of a vielbein is coupled to the heat current density,
if it is defined by the product of the time derivative and velocity but not that of the Hamiltonian and velocity [2].
This observation enables us to define the following quantities:
(a) Heat magnetization [2]: We provide the thermodynamic definition with use of a torsional magnetic field.
It gives an important contribution to the thermal Hall conductivity. (b) Thermal conductivity [3]:
We derive the Kubo formula with use of a torsional electric field.
It is justified by the Wiedemann-Franz law at low temperature. (c) Heat polarization [4]:
We derive the Berry-phase formula in the same manner as in the charge polarization.
In contrast to the charge-heat analogy, it does not appear simultaneously owing to the Mott rule.
These quantities can be systematically calculated even in disordered or interacting systems
by using the Keldysh formalism in curved spacetime [3].
[1] J. M. Luttinger, Phys. Rev. 135, A1505 (1964).
[2] A. Shitade, arXiv:1310.8046.
[3] A. Shitade, arXiv:1310.8043.
[4] A. Shitade, in preparation.
- 2013/12/18(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 吉井涼輔 (京都大学基礎物理学研究所)
- Title
- Transport in Aharonov-Bohm ring with embedded quantum dot
- Outline
- The Kondo effect is the entanglement of an impurity spin with conduction electrons
as the temperature is lowered below the Kondo temperature.
One interesting and highly nontrivial extension of the basic Kondo model
involves an Aharonov-Bohm (AB) ring with an impurity
in the upper arm and interference with a lower “reference arm”.
Using the AB ring, the transmission phase of an electron passing
through a quantum dot can be measured.
The previous studies stated that a formula for the conductance
where all interaction effects were contained in the single-electron T matrix
for the corresponding single-channel Kondo model.
Starting from the Kubo formula,
we show that the conductance cannot be written by the linear term of T-Matrix,
which is inconsistent with the previous study [1].
Here we rederive them using Kubo formalism, generalize them
to finite temperature and arbitrary density in the leads,
and examine the condition in which the formula given by the previous study is valid [2].
[1] W. Hofstetter, J. Konig, and H. Schoeller, PRL, 87, 156803 (2001).
[2] Y. Kamijani, R. Yoshii, and I. Affleck, PRB, 88, 245104 (2013).
- 2013/12/11(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 佐野 友彦 (京都大学基礎物理学研究所)
- Title
- Roles of Dry Friction in Fluctuating Motion of Adiabatic Piston
- Outline
- Recent developments in experimental technique enable us to control small systems and non-equilibrium systems to clarify their
thermodynamic structures, indetail. One of the most important applications of manipulation techniques for small systems is the
design of nano-machines or sub-micron machines. The difficulty to realize efficient small machines is the existence of dry friction
when two solids are in contact, because the dry friction wears down the small machines. Because the dry friction is ubiquitous
throughout nature, to control systems under dry friction is indispensable to make small machines [1]. Experiments for macroscopic
systems under the dry friction reveal that the dry friction has an important role to rectify unbiased fluctuations, i.e. to extract
work from an equilibrium environment [2].
Although the dry friction plays essential roles in non-equilibrium transport, the energetics for the systems under the dry friction
has been elusive so far.
In this seminar, we consider fluctuating motion of an adiabatic piston under dry friction to clarify the roles of dry friction in
non-equilibrium steady states [3]. We clarify that the dry friction can reverse the direction of the piston motion and causes a
discontinuity or a cusp-like singularity for velocity distribution functions of the piston. We also show that the heat fluctuation relation is modified under the dry friction. If time allows, we report the recent progress on the fluctuating heat
engines under dry friction.
[1] R. Guerra, U. Tartaglino, A. Vanossi and E. Tosatti, Nature Materials 9, 634 (2010).
[2] A. Gnoli, A. Petri, F. Dalton, G. Pontuale, G. Gradenigo, A. Sarracino, and A. Puglisi, Phys. Rev. Lett. 110, 120601(2013).
A. Gnoli, A. Sarracino, A. Puglisi and A. Petri, Phys. Rev. E 87, 052209 (2013).
A. Sarracino, A. Gnoli, and A. Puglisi, Phys. Rev. E 87, 040101(R) (2013).
[3] T. G. Sano and H. Hayakawa, arXiv:1309.7700.
- 2013/11/18(Mon) 16:30 - @Seminar Room K202, Yukawa Institute
- Speaker
- 仲田 光樹 (京都大学基礎物理学研究所)
- Title
- Non-Equilibrium Quantum Spin Transport Theory Based on Schwinger-Keldysh Formalism; Related Topics to Spin Current
- Outline
- Spin currents, namely transports of magnetizations, have been attracting special attentions from viewpoints of
fundamental science and potential applications to quantum devices.
We then present non-equilibrium quantum spin transport theories based on Schwinger-Keldysh formalism.[1,2]
In particular, we focus on the experimentally established method for the generation of spin currents, spin pumping;[3]
beyond a phenomenological discussion, we reveal the microscopic mechanism and clarify the origin of the spin current.[#]
After that, if time (and collaborator) permits, we would like to show our latest project;[2] Josephson effect of magnon
condensates under quantum phases. This macroscopic phenomenon is analogous to the magnon Hall effect[4] and it is the
fruits of macroscopic quantum effects where spin currents are carried by magnon condensates owing to a certain quantum
phase,[5] which works as a driving force. Lastly, we would like to discuss the resultant possibility for the emergence of
persistent spin currents[6] and theoretically propose a method to experimentally realize it.
----------
References
----------
[1] K. Nakata and G. Tatara. J. Phys. Soc. Jpn., 80 (2011) 054602.
K. Nakata, J. Phys. Soc. Jpn. 81 (2012) 064717.
K. Nakata, J. Phys.: Condens. Matter. 25 (2013) 116005, and references therein.
[2] K. Nakata,K. A. van Hoogdalem, P. Simon and D. Loss, in preparation.
[3] Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin, Rev. Mod. Phys. 77 (2005) 1375.
[#] This would become the main part of this talk.
[4] Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Science 329 (2010) 297.
[5] F. Meier and D. Loss, Phys. Rev. Lett. 90 (2003) 167204.
[6] D. Loss, P. Goldbart, and A. V. Balatsky, Phys. Rev. Lett. 65 (1990) 1655.
F. Schutz, M. Kollar, and P. Kopietz, Phys. Rev. Lett. 91 (2003) 017205.
- 2013/11/13(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 村上 亮 (京都大学基礎物理学研究所)
- Title
- 等温弾性球の正面衝突における弾性振動の影響
- Outline
- 物体の衝突は野球やゴルフなどのスポーツからPM2.5のような微粉末中においてまであらゆるところで見られるが,
特に散逸の小さい場合[1]や微小物体の場合[2]には重心と内部自由度の結合により思いがけない振る舞いが見出される.
我々は等温弾性球モデルを用いたシミュレーションにより,衝突における内部自由度(弾性振動)の影響を詳細に調べた.
まず温度0の場合において,はね返り係数の衝突速度依存性に特徴的な振動構造を見出した.
このとき固有振動の励起エネルギーを調べると,接触時間の逆数が固有周波数の整数倍のときにピークとなることから,
一種の共鳴が起きていることがわかった.
また,熱振動する球の衝突では,はね返り係数が固有振動の初期位相に対し三角関数のように振る舞い,
結果としてはね返り係数が1を超える「超弾性衝突」が生じることを確認した.さらにこの依存性を摂動論により導出した.
セミナーではサイズ依存性,接触力,モードトランスファー,ゆらぎの定理などに関する結果についても詳述する.
[1] P. Müller, M. Heckel, A. Sack, and T. Pöschel, Phys. Rev. Lett. 110, 254301 (2013).
[2] H. Kuninaka and H. Hayakawa, Phys. Rev. E 79, 031309 (2009).
- 2013/11/06(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 大信田 丈志 (鳥取大学 工学部)
- Title
- Analytical calculation of the displacement correlation tensor: from single-file diffusion to two-dimensional glassy liquids
- Outline
- Glassy and granular materials [1] exhibit slow dynamics due to "crowdedness":
the shortage of space forbids free motion and compels the particles either to wait still or move cooperatively,
leading to what is called dynamical heterogeneity.
The cooperative motion can be quantified in terms of four-point space-time correlations [2].
Although analytical calculation of four-point correlation has been reported for elastic solids
and a certain kind of lattice models [3],
it has been difficult to treat them analytically in more realistic models of glassy liquids,
such as the system of Brownian particles with short-ranged repulsive interaction.
Here we report our recent work on systems of repulsive Brownian particles,
demonstrating that the two-dimensional displacement correlation tensor,
which is a kind of four-point correlation, can be calculated
by extending the one-dimensional label variable method [4,5] to the higher dimensions.
The method consists in focusing on the Lagrangian correlation of inter-particle vacancy fluctuation,
as opposed to the Eulerian correlation that is used in the standard mode-coupling theory of glassy liquids.
In the one-dimensional case, the linear theory with the label-variable method
reproduces the established result on the anomalous behavior of the single-file diffusion [4].
A correction is given by the nonlinear theory embodied in a version of mode-coupling theory
without violation of the fluctuation-dissipation theorem [5].
Subsequently, the whole theory is adapted from the one-dimensional to the two-dimensional setup.
The two-dimensional linear theory yields a flow pattern consisting of a pair of vortices
(see, for example, Fig. 8 in Ref. [6]); with a certain additional assumption,
it also predicts that the mean-square displacement is nearly proportional to the time
with a logarithmic correction term, being qualitatively consistent with a precedent result
on diffusion in two-dimensional lattice systems [7].
[1] http://www2.yukawa.kyoto-u.ac.jp/ws/2013/pggm/
[2] L. Berthier & G. Biroli: Rev. Mod. Phys. 83, 587 (2011)
[3] C. Toninelli et al.: Phys. Rev. E 71, 041505 (2005)
[4] Ooshida T. et al.: J. Phys. Soc. Jpn. 80, 074007 (2011)
[5] Ooshida T. et al.: arXiv:1212.6947
[6] B. Doliwa & A. Heuer: Phys. Rev. E 61, 6898 (2000)
[7] H. van Beijeren & R. Kutner: Phys. Rev. Lett. 55, 238 (1985)
- 2013/10/30(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 今村 卓史 (東京大学 生産技術研究所)
- Title
- Replica approach to the 1d KPZ equation
- Outline
- The Kardar-Parisi-Zhang(KPZ) equation is a prototypical stochastic partial differential equation
of surface growth.
Recently significant progress has been achieved in the KPZ equation especially in one-spatial dimension.
In 2010, Sasamoto-Spohn and Amir-Corwin-Quastel independently
obtained the exact solution of the height distribution.
It turned out that in the long time limit it converges to the GUE Tracy-Widom distribution
in the random matrix theory.
In this seminar I will talk about recent progress of this topic especially focusing
on our recent results[1,2,3].
The replica approach is a powerful tool to obtain the exact height distribution.
In this approach we use an intriguing connection between the 1d KPZ equation and 1d Bose gas system
with delta function attractive interaction where we can use the Bethe ansatz results.
This is based on joint work with Tomohiro Sasamoto and Herbert Spohn.
[1] TI and T. Sasamoto, Phys. Rev. Lett. 108, 190603, 2012
[2] TI and T. Sasamoto, J. Stat. Phys. 150, 908-939,2013
[3] TI, T. Sasamoto and H. Spohn, J. Phys. A, 56,355002,2013
- 2013/10/28(Mon) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Frederic van Wijland (Universite Paris Diderot-Paris 7)
- Title
- Brownian dynamics can be glassy or trivial
- Outline
- As the density of an assembly of colloids is increased,
its dynamics dramatically slows down.
This phenomenon is attributed to the trapping of the system
into the deepest structures of some energy landscape.
We wish to question this view by examining the role of the dynamics in visiting this energy landscape.
We will compare a variety of evolution rules sampling the same equilibrium state,
some of which will exhibit expected glassiness, some others won't.
- 2013/09/11(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Mahesh Bandi (沖縄科学技術大学院大学)
- Title
- Fragility and hysteretic creep in frictional granular jamming
- Outline
- The Jamming framework was proposed as an overarching,
unifying description governing the behavior of a wide variety of disordered materials.
Being amenable to theoretical treatment, several early studies concentrated on idealized frictionless systems.
Growing number of studies, however, conclusively demonstrate inter-particle friction
substantially alters jamming behavior. In this talk, we present an experimental study where a loose,
granular pack comprising a two-dimensional, bi-disperse system of frictional disks subjected to quasi-static,
uniaxial compression (loading) and decompression (unloading).
We first verify numerical results demonstrating jamming onset at packing fractions below random close packing
with increasing friction.
Next we show, the pressure scaling is remarkably different between the first and subsequent loading cycles.
In the first cycle as the system's boundaries are moved in to achieve an increasingly tighter packing,
a fragile state is observed where the pressure exhibits an exponential rise over a range of packing fractions,
followed by a deviation from exponential scaling. This exponential rise in pressure
is simultaneously reflected in an exponential decrease in particle displacements
over the same range of packing fractions,
implying the simultaneous existence of jammed and unjammed clusters in the granular pack.
Finally we show, under repetitive loading and unloading,
the critical packing fraction at which the granular pack jams progressively increases to higher values,
thereby exhibiting creep. At the same time the pressure curves
for the loading-unloading cycles exhibit hysteretic responses.
We experimentally trace the source of all these effects to inter-particle contact friction.
- 2013/06/17(Mon) 16:30 - @Seminar Room K202, Yukawa Institute
- Speaker
- 布能 謙 (東京大学大学院理学系研究科)
- Title
- Quantum Fluctuation Theorems under Measurement and Feedback control
- Outline
- Fluctuation theorems and Jarzynski equalities have attracted considerable interest,
since they give equalities on physical quantities in nonequilibrium processes,
in contrast with the conventional second law, which gives inequalities.
On the other hand, Maxwell's demon has attracted many researchers in such diverse fields
as (quantum) information theory and statistical mechanics for over one and half century.
Maxwell's demon is one type of a feedback controller that can measure the system's microscopic degrees of freedom,
and control the system via feedback depending on the measurement outcome.
Then, the feedback controller has more access to the system than just controlling the macroscopic degrees of freedom,
which result in work extraction from the system beyond the conventional second law [1].
Associated with the modification of the second law, fluctuation theorems are also modified
by including information contents for a classical system [2].
A quantum version of the generalized quantum Jarzynski equality was discussed by considering a projective measurement
on the system followed by a classical error [3].
However, we need to consider a general quantum measurement $M_{k}$
to discuss the quantum nature of the measurement and the feedback.
In this seminar, we consider quantum fluctuation theorems under measurement and feedback control
by taking into accout the information gain or the quantum-classical (QC-) mutual information content,
which correctly characterizes the acquired knoledge of the system due to the measurement.
The obtained equality repsoduce the second law of thermodynamics
under measurement and feedback control obtained in Ref. [1].
[1] T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 080403 (2008).
[2] T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012).
[3] M. Morikuni and H. Tasaki, J. Stat. Phys. 143, 1 (2011).
- 2013/06/05(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 李 宰河 (東京大学大学院理学系研究科)
- Title
- 弱測定の数理とその超精密測定への応用
- Outline
- 量子力学におけるObservableの値として従来知られていたスペクトル値および期待値の複素数への拡張として、
近年「弱値」の概念が注目を浴びており、実験的にはこれを「弱測定」によって得ることができるとされている。
近年、実際に「弱測定」による超精密測定実験の成功が報告されている一方で、
その立脚するところの議論は多く近似を含んだ荒削りなものである点で不満が多く、
確固たる理論的基盤の確立が急務であった。
本講演では、近似や定義の不明瞭さを一切排した数学的に厳密な「弱測定」の取り扱い方を提示した上で、
応用においても、「弱測定」は従来のvon Neumannモデルの量子測定では不可能であった微細な物理現象の検出等に有用であることを示す。
- 2013/05/29(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- 山田康博 (東京大学大学院工学系研究科)
- Title
- Resolution effects on the current statistics in the resonant level model
- Outline
- Recently, it has attracted much attention to investigate the distribution of current in nonequilibrium mesoscopic systems.
For instance, the current noise, which is the variance of the distribution, has been extensively studied as well as the average current.
It is, however, often observed that the measured noise is larger than the inherent one expected from theories.
We here consider the puzzle.
In an actual experiment, the distribution is not only determined by the observed system but also by the measurement device.
Although the full counting statistics has been used for the calculation of the distribution,
the influence of the device has not been fully considered.
Then, it is necessary to theoretically deal with the inevitable issues of the device, such as resolution,
for better comparison of theory and experiment.
In this study, we propose the quantum two-point measurement with limited resolution.
Our method is equivalent to the ordinary full counting statistics in an ideal condition,
but can consider resolution of the device in the other cases.
Using this method, we analyze resolution effects on the distribution of current flowing a resonant level coupled to two reservoirs.
In the unbiased measurement case, it is found that the measured noise becomes a sum of the inherent noise and the excess one.
Since the excess noise is always positive and increased by poor resolution,
the measured noise is always larger than the inherent noise, which is consistent with experiments.
Furthermore, we find a universal exponential curve in the deviation from the Johnson-Nyquist relation
between the measured current and noise for low temperature and low conductance.
- 2013/05/08(Wed) 16:00 - @Seminar Room K202, Yukawa Institute
- Speaker
- Meheboob Alam (Jawaharlal Nehru Center for Advanced Scientific Research/YITP)
- Title
- Microcopic and Macroscopic Properties of Granular Poiseuille Flow from Event-driven Simulations
- Outline
- Event-driven simulations are conducted for an inelastic smooth hard-disk system
to understand the effects of system parameters and wall-roughness
on the microscopic (particle-level) and macroscopic behaviour of gravity-driven granular Poiseuille flow (GPF).
The microscopic properties like (a) the velocity distribution functions (VDF), (b) the pair correlation function
and (c) the spatial velocity correlations have been measured for dilute as well as dense systems.
The Maxwellian is found to be the leading order VDF over a wide range of densities in the quasi-elastic limit for GPF with smooth walls.
The above observation holds even in a dilute GPF for which the Knudsen number belongs to the transitional flow regime.
The distribution functions become asymmetric with increasing dissipation at any density,
and the onset of density-waves seems to be responsible for such asymmetries.
At high densities, the flow degenerates into a dense plug
(where the density approaches its maximum packing limit and the shear-rate is negligibly small)
around the channel centerline and two shear-bands (where the shear rate is high and the density is low) near the walls.
The high-velocity tails of VDFs undergo a transition from Gaussian in the quasi-elastic limit to power-law distributions
with increasing dissipation within the dense plug.
It appears that the combined effect of enhanced density and velocity correlations around the channel-centerline
with increasing inelastic dissipation is responsible for the emergence of non-Gaussian power-law tails of VDFs.
The results on macroscopic properties like (a) the hydrodynamic fields, (b) the non-Newtonian rheology and
(c) the slip boundary condition will also be discussed.
- 2013/05/01(Wed) 13:30 - @Seminar Room K202, Yukawa Institute
- Speaker
- 薮中 俊介 (京都大学大学院 理学研究科)
- Title
- Interface approach to self propelled motion of a fluid droplet under chemical reaction
- Outline
- By means of interface approach, we study self-propelled dynamics of a droplet
due to a Marangoni effect and chemical reactions.
The equation for the migration velocity of the center of mass of a droplet
is derived in the limit of an infinitesimally thin interface.
We found that there is a bifurcation from a motionless state to a propagating state of droplet
by changing the strength of the Marangoni effect.
If time allows, I would like to discuss interface motion
in semidulute polymer solutions or lamellar dynamics in micro-phase separated diblock copolymer systems.
- 2013/04/24(Wed) 16:30 - @Seminar Room K202, Yukawa Institute
- Speaker
- 伊丹 將人 (京都大学)
- Title
- 断熱ピストン問題の熱浴模型依存性
- Outline
- 断熱可動壁で区切られたふたつの領域に多数の粒子を閉じ込め、両側の圧力が等しくなるように制御しても、
温度差があると断熱可動壁はある方向に動く。
この運動は断熱可動壁のゆらぎを介したエネルギーの漏れによって生じるが、運動の方向は熱力学の法則からは決まらず [1]、
両側の圧力が等しいため流体力学の枠組みでも説明できない。
この現象は断熱ピストン問題と呼ばれ、流体が希薄気体の場合には、
運動論による解析 [2]、数値実験[3]、現象論の提案[4]などがなされており、断熱可動壁は高温側に動くことが示されている。
本セミナーでは、温度と圧力を制御する熱浴として常に平衡状態にある自由粒子を用いて、
断熱ピストン問題を一般の相互作用する多粒子系というミクロな記述にもとづく非平衡統計力学の立場から考察する。
まず、線形応答関係を利用することで問題を平衡ゆらぎの解析に帰着させ、
さらに縮約を行うことで線形応答関係式を断熱可動壁に関わる物理量だけで表す。
そして、平衡状態における物理量の時間発展方程式を用いて、この関係式を計算することで、
定常状態における断熱可動壁の速度を導出し、数値実験によって正当性を確かめる。
以上の解析により、断熱ピストン問題は理解できたように見えるが、
温度と圧力を制御する熱浴としてランジュバン熱浴と一定外力を用いるとピストンは動かないという帰結が得られてしまう。
最後に、この熱浴模型の依存性について考察する。
[1] H. Callen, Thermodynamics and an Introduction to Thermostatistics,2nd ed. (Wiley, 1985).
[2] C. Gruber and J. Piasecki, Physica A 268, 412 (1999).
[3] E. Kestemont, C. Van den Broeck, and M. Malek Mansour, EPL. 49,143(2000).
[4] A. Fruleux, R. Kawai and K. Sekimoto, Phys. Rev. Lett. 108, 160601(2012).
- 2013/04/10(Wed) 16:00 - @Seminar Room K206, Yukawa Institute
- Speaker
- 小林 未知数 (京都大学大学院理学研究科)
- Title
- Statistical mechanics of non-Abelian topological defects
- Outline
- Topological defects appear in various physical systems such as condensed matter,
soft matter, cosmology, optics, high-energy physics, and so on,
playing a crucial role to determining both statistical and dynamical properties of such systems.
Sometimes, the microscopic properties of topological defects are strongly influenced by their topological properties.
Especially, when the topological property is characterized by the non-Abelian group,
one of the most intriguing behavior can be seen; "topological invariance" (topological charge) of defects
is no longer invariant and defects exchanges their charges with different defects due to their non-commutativity.
In my talk, I show the two examples of non-Abelian defects and their non-trivial statistical properties caused
by the above non-Abelian propety.
The first example is line-wall defects coexisting system
in which line and wall defects interchanges their charges and both defects always coexist.
The second example is non-Abelian line defect system in which the charge of defect interchanges
through their braiding dynamics. In 2-dimensional system, such non-Abelian properties become drastically appears.
In the former case, the 2nd ordered phase transition with the spontaneous symmetry breaking
due to the discrete symmetry and the Kosterlitz-Thouless transition due to the paring of line defects
(point defects in 2D) occurs simultaneously, and the Kosterlitz-Thouless transition is prohibited in the latter case.