- Weak Galilean invariance as a selection principle for stochastic coarse-grained diffusive models
- Speaker: Andrea Cairoli (Imperial College London, South Kensington Campus)
- Date: 2018-02-07 (Wed.) 13:30 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

Galilean invariance states that the equations of motion of closed systems do not

change under Galilei transformations to different inertial frames. However, real

world systems typically violate it, as they are described by coarse-grained models,

that integrate complex microscopic interactions indistinguishably as friction and

stochastic forces. This leaves no alternative principle to assess a priori the

physical consistency of a given stochastic model. In this talk, I use the

Kac-Zwanzig Hamiltonian model of Brownian motion to clarify how Galilean invariance

is broken during the coarse graining procedure to derive stochastic equations and

derive a set of rules characterizing systems in different inertial frames, called

weak Galilean invariance. Several stochastic processes, generating both normal

and anomalous diffusion, are shown to be invariant in these terms, except the

continuous-time random walk, whose correct invariant description is discussed.

These results are particularly relevant for the modelling of biological systems,

as they provide a theoretical principle to select stochastic models of complex

dynamics prior to their validation against experimental data.

- 生物系の理論事始め (in Japanese)
- Speaker: 大野 克嗣 (Univ. of Illinois at Urbana-Champaign/京都大学 基礎物理学研究所)
- Date: 2017/12/25 (Mon.) 10:30 – 2017/12/26 (Tue.) 16:15
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

生物系の理論の窮極的目的は理論/数理物理的に生物を理解することだ．もちろ

ん，現状はこれに程遠い．そこで今何をするか？ 生き物の現象論的要約を試み，

生物系のありうべき理論的な核を抽出することを試みる．講義参加者はごちゃご

ちゃしたことは嫌いだろうから，生物の実際にあまり深入りはしない(もちろん

自前の体系を作りたい人にこれは不可避である)．「非線形な世界」(東大出版

2009)の最終章に書いたことの部分的実現を目指す．

おおよそのプラン:

(1) 生物物理，数理生物や複雑系研究はほぼどうでもいい．

(2) では何をするか？ 統合自然誌とは何か．

(3) 生物系の際立った特徴．

(4) パストゥールの原理から何が従いうるか？

(5) 次には何をすべきか？

(a) 生き物の現象論的整理のさらなる継続深化．

(b) 理論の展開の助けになるような数理的モデルの構築．

時間割：全て講義

12月25日 10:30～12:00、13:00～14:30、14:45～16:15、16:30～18:00

12月26日 10:30～12:00、13:00～14:30、14:45～16:15

- Quantum gas in the fast forward of adiabatically expanding cavities: force and equation of states
- Speaker: Katsuhiro Nakamura (National University of Uzbekistan)
- Date: 2017/12/20 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

Applying the idea of fast forward of adiabatic control of 1D confined

systems, we investigate the nonequilibrium equation of states of an ideal

quantum gas (Fermi gas) confined to the rapidly-dilating soft-wall and

hard-wall cavities. We show the fast-forward variants of Poisson’s adiabatic

equation and Bernoulli’s formula which bridges the force and internal energy.

Confining ourselves to the thermally-isolated isentropic process and

using the exact solution of the von Neumann equation, statistical means of the

adiabatic and non-adiabatic (time-reversal symmetric) forces are evaluated in both

low-temperature quantum-mechanical and high temperature quasi-classical regimes.

Reflecting the fact that the fast-forward dynamics is population-preserving

cooling or heating process, the state variables such as the statistical mean of

force, cavity size and effective temperature are not quasi-static, but rapidly-changing

variables. We elucidate the quantum non-adiabatic (NAD) contributions to the

equation of states. The NAD contributions are proportional to the acceleration of

cavity size and square of its velocity. We also revealed the condition when NAD

contribution overwhelms the adiabaticone and thoroughly changes the feature of

the equilibrium equation of states.

- Jamming and crystallization of deformable particle systems
- Speaker: Massimo Pica Ciamarra (Nanyang Technological Univerisy, Singapore)
- Date: 2017/10/5 (Thu.) 16:30 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

Biological cells and polymeric particles such as star polymers,

dendrimers and microgels change volume and shape when compressed by

their neighbors at high density. In this regime the energy of a

particle depends on its shape, which is fixed by its close neighbors,

so that particles interact via a many-body potential. We study the

two-dimensional melting of a model of confluent tissues that captures

the many-body nature of the interaction, exploring the role of

particles’ softness. We show that, depending on the softness of the

particles, the zero temperature ground state could be of solid,

hexatic or liquid type. On increasing the temperature, the solid melts

either via a one-step first-order transition, if particles are stiff,

or via a two-step process with a continuous solid-hexatic transition

and a consecutive first-order hexatic-liquid transition, if particles

are soft.

- Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling
- Speaker: Kosuke Ito (Nagoya Univ.)
- Date: 2017/6/5 (Mon.) 14:45 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

In quantum thermodynamics, effects of finiteness of the baths have been lessconsidered. In particular, there is no general theory to focus on finiteness ofthe baths of arbitrary multiple conserved quantities. Thus, we focus on how theoptimal performance of generalized heat engines with multiple quantities altersin response to the size of the baths. Conventionally, the size of the baths inquantum thermodynamics has been given in terms of the number of identical copiesof a system, which does not cover even such a natural scaling as the volume. Inconsideration of the asymptotic extensivity, we deal with a generic scaling ofthe baths to naturally include the volume scaling. Based on it, we derive thebound for the performance of generalized heat engines reflecting finite-sizeeffects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine givenby this bound. Finally, applying the obtained general theory, we deal withsimple examples of generalized heat engines. 1D Ising spin chain model and a toymodel of two-level particles illustrate strange behaviors of the finite-sizeeffects. The other example is a heat engine with two baths composed of an idealgas exchanging particles, where the volume scaling is applied. The resultimplies that the mass of the particle explicitly affects the performance of thisengine with finite-size baths. - References:
- K. Ito and M. Hayashi, arXiv:1612.04047

- Prethermalization, thermalization, and recurrence in one dimensional Bosons
- Speaker: Eriko Kaminishi (Univ. of Tokyo)
- Date: 2017/5/22 (Mon.) 14:40 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

Dynamics of an isolated quantum system has attracted much interest both in experiment and theory due to their potential to testing the foundation of quantum statistical mechanics.

In contrast to classical systems, relaxation occurs even in a few-body quantum system due to quantum entanglement. A few-body system can also exhibit the recurrence phenomenon in an accessible timescale in experiment. Moreover, we found a new mechanism of prehtermalization in a few-body quantum system, which we call entanglement prethermalization. Prethermalization is a phenomenon that the system relaxes to a quasi-stationary state before reaching thermal equilibrium, which is usually associated with the presence of nearly conserved local quantities. In the entanglement prethermalization, highly nonlocal quantum entanglement between the subsystems strongly affects the local property of the (quasi) stationary state.

In this talk, we discuss those intriguing quantum dynamics in one-dimensional bosons by studying the Lieb-Liniger model. - References:

- Numerical study of granular splash and force propagation in granular bed
- Speaker: Takahiro Tanabe (Hiroshima Univ.)
- Date: 2017/5/17 (Wed.) 10:30 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
Abstract:

Granular materials, such as powder, agricultural grains and sand, play important roles in our life. Further, their collision processes are taken as one of fundamental processes observed in natural fields. In particular, the way how sand grains are ejected from ground surface when wind-blown grains hit them is an important issue for understanding stationary sediment transport. The whole process, starting from the initial impact of a grain and ending with ejection of many grains, are shortly called “splash process”, and the transport of grains near the surface is sustained by splash process.

For this reason, splash process has been extensively studied with experiments, and previous experiments have shown the relations between the incident angle/speed of the impacted grain and ejection grains’ angle/speed [1]. We have simulated the splash process with similar system to previous experiments using the discrete element method (DEM) and obtained the qualitative agreement with these experimental results. Moreover, we found that ejection grain dynamics varies depending on their ejection timing after the initial impact, which is reflected to the drastic change of the ejection velocity distributions [2]. This result suggests that the way of impact propagation along and beneath the granular bed surface varies according to the timing after the impact.

For the next step, we have investigated the relation between the grain ejection process and the force propagation process beneath the granular bed surface induced by the impact of a grain onto the granular bed surface. To elucidate this relation, we have focused on the “force path” which gives the connection from the initially impacted grain through force propagation to ejected grains by numerically analyzing binary contacts inside the bed with simple definition. We will show the relation between force propagation process and ejection process taking care of inner dynamics of granular bed.- References:
- M. Ammi, et al., Phys. Rev. E, 79, 021305, (2009)
- T. Tanabe, et al., Phys. Rev. E, 95, 022906, (2017)

- Fracture in Different Scales: A Statistical Mechanical Approach
- Speaker: Subhadeep Roy (Univ. of Tokyo)
- Date: 2017/4/26 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

Fracture is a complex phenomenon involving large span of

time and length scales, starting from atomic scale or laboratory scale

to geological scale like earthquake. A failure process can take place

showing precursory rupture events, or catastrophically without showing

such precursor. Also the rupture events might show correlation among

themselves or might happen in a random manner. So the important

question is:What are the physical criteria that govern the mode of

failure ? In statistical mechanics, disorder systems and systems out

of equilibrium are extensively studied in the last decade. So it will

be interesting to study fracture in statistical mechanical point of

view. The talk deals

with the implementation of two main factors, disorder and stress

release range, that guides failure process. A a statistical model

namely Fiber Bundle Model is used to study the effect of above two

parameters on the failure process, starting from laboratory scale to

earthquake. - References:

Efficiency bounds on thermoelectric transport in magnetic fields: the role of inelastic processes

- Speaker: Kaoru Yamamoto (Univ. of Tokyo)
- Date: 2017/4/12 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

It has been argued that breaking time-reversal symmetry which can make the Onsager matrix asymmetric is a way to achieve a high thermoelectric efficiency. Benenti et al. recently claimed [1] that in this case one can achieve the Carnot efficiency with a finite power, which appears to contradict the second law of thermodynamics.

Many studies tackled this problem in individual models (see Refs. [2-4] for example) as well as in quite general cases [5,6].

In order to obtain an asymmetric Onsager matrix, we consider an Aharonov-Bohm ring threaded by a magnetic flux, incorporating electron-phonon inelastic scattering [7]. We find that breaking time-reversal symmetry in the presence of the inelastic process can significantly enhance the figure of merit for delivering electric power by supplying heat from a phonon bath [8]. The efficiency is bounded by the non-negativity of the entropy production of the original three-terminal junction [8], which is consistent with the result in [5,6]. - References:

[1] G. Benenti, K. Saito, and G. Casati, Phys. Rev. Lett. 106, 230602 (2011).

[2] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. Lett. 110, 070603 (2013).

[3] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. X 5, 031019 (2015).

[4] K. Proesmans and C. Van den Broeck, Phys. Rev. Lett. 115, 090601 (2015).

[5] N. Shiraishi, K. Saito and H. Tasaki, Phys. Rev. Lett. 117, 190601 (2016)

[6] N. Shiraishi and H. Tajima, arXiv:1701.01914 (2017).

[7] O. Entin-Wohlman and A. Aharony, Phys. Rev. B 85, 085401 (2012).

[8] K. Yamamoto, O. Entin-Wohlman, A. Aharony, and N. Hatano, Phys. Rev. B 94, 121402 (2016)

- Nonequilibrium Steady States in Weakly Coupled Quantum Spin Systems
- Speaker: Ayumu Sugita (Osaka City Univ.)
- Date: 2017/4/5 (Wed.) 16:00 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:

熱流のある非平衡定常状態では、温度勾配に比例して熱流が流れるというフーリエ則が通常成り立っている。これは経験的には非常に普遍性の高い法則であるが、簡単な理論モデルではむしろ温度勾配を持たない定常状態が現れることが多く、フーリエ則の成立条件については完全には分かっていない。一般にはフーリエ則が成立するためには系の非可積分性（カオス性）が必要であると言われることが多いが、それが正しいとすると、温度勾配を持つノーマルな熱伝導状態をミクロな視点から解析的に調べることは非常に困難に思える。

我々は、温度勾配を持つ定常状態に対して解析的知見を得るため、弱結合量子系の非平衡定常状態を扱う摂動論を開発した。特に、スピン1/2の1次元スピン鎖において、温度勾配が存在する条件は非可積分性とは異なることを見出した。また、温度勾配を持つ系では非平衡特有の3点相関が現れ、その形は弱結合極限で相互作用に依らない普遍的な形を取ることを示した。これらの結果について解説する。

- References:

T. Ishida and A. Sugita, J. Phys. Soc. Jpn. 85, 074006(2016)