Official web site of Takeuchi Lab, Univ. Tokyo

外部エネルギーを用いて自己駆動する粒子系はアクティブマターと呼ばれ、フロッキング転移、モティリティ誘起相分離、ミクロ相分離といった非平衡特有の相転移現象が生じることが知られている [1]。このような相転移の性質は、古典モデルのシミュレーションや人工粒子系の観察などにより、近年理解が進んできた。一方、量子系に目を向けると、冷却原子系に代表される人工量子系の制御技術の発展に伴い、エネルギー流入や散逸を伴う開放量子系の研究が盛んに進められている。特に、非エルミートハミルトニアンによる有効記述を用いて、特有の臨界現象やトポロジカル相などが議論されてきた [2]。

このような背景のもと我々は、量子多体系におけるアクティブマターモデルを初めて提案し、古典系での自己駆動力が量子系では非エルミート性として表現されることを明らかにした [3]。このモデルでは、自己駆動力に起因した量子相転移が生じ、フロッキング状態やモティリティ誘起相分離状態の量子対応物が現れることがわかった。さらに、量子相転移が古典確率過程モデルにおける動的相転移に対応することを見出し、この対応を相図の解釈に利用した。また、このモデルは散逸を導入した光格子中の冷却原子気体によって実現できると考えられ、その実装方法も提案した。

セミナーでは、アクティブマターで生じる相転移について概説したあと、古典アクティブマターモデルに基づいて量子モデルを構築する方法を説明し、量子モデルの数値シミュレーション結果について議論する。

[1] G. Gompper et al., J. Phys. Condens. Matter 32, 193001 (2020).
[2] Y. Ashida, Z. Gong, and M. Ueda, arXiv:2006.01837.
[3] K. Adachi, K. Takasan, and K. Kawaguchi, arXiv:2008.00996.

量子多体系でパラメータをクエンチさせて非平衡ダイナミクスを調べると、そこに動的スケーリングが現れる場合があり、その普遍性クラスが活発に研究されている。特にここ数年、冷却原子系の実験でスピン相関関数や運動量分布の動的スケーリングが実験的に観測されている[1,2,3]。このような背景のもと、我々は古典系で知られている揺らぐ界面の動的スケーリング、つまりFamily-Vicsek(FV)スケーリングに注目して、孤立量子多体系における界面荒さのFVスケーリングを理論的に研究した。具体的には1次元Bose-Hubbardモデルを用いて、古典系の揺らぐ流体力学とKardar-Parisi-Zhang方程式のアナロジーから界面高さ演算子を導入して、その界面荒さの時間発展をFVスケーリングの視点から調べた。本セミナーでは論文[4]の結果に基づいてその詳細を議論する。

[1] M. Prüfer et al., Nature 563, 217 (2018).
[2] S. Erne et al., Nature 563, 225 (2018).
[3] J. A. P. Glidden et al., arXiv:2006.01118.
[4] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 124, 210604 (2020).

It is well known that external perturbations evolve a frictional granular pack jammed in an initial metastable configuration to an eventual stable one. Beneficial in achieving efficient packing, athermal perturbations can also cause catastrophic failure. Understanding pack response to perturbations naturally carries both fundamental and applied significance. In a related context, the power law pressure increase against packing fraction is considered one signature of the frictionless jamming transition. In contrast, independent studies reveal frictional jamming exhibits an initial exponential pressure rise before deviating towards the putative power law. The range of packing fraction values over which pressure rises exponentially is marked by a marginally stable solid (fragile state) sensitive to perturbations. In this talk, I report experiments on frictional granular pack pressure response to controlled perturbations in this fragile state. In particular, I will deduce an empirical result from the experimental data which establishes a close correspondence between this classical (frictional jamming) problem and a well known quantum effect for electron transport in amorphous semiconductors.

Ray systems, or set of radial streaks that encircle an impact crater, became known shortly after the advent of the telescope, perhaps in 1647, when Johannes Hevelius published what might have been the first map of the Moon to show them. Although they were recognized as settled ejecta, that is, deposits of debris thrown out when a meteorite impacts the surface of a planetary body, their origin proved to be the sort of question for which competing theories abound to date. Motivated by observations of ray systems in planetary cratering, we study an analog system: granular cratering. In classical experiments of granular cratering, a ball dropped on an evened-out bed of grains ends up within a crater surrounded by a uniform blanket of ejecta. We show that the uniform blanket of ejecta changes to a ray system where the surface of the granular bed includes undulations, a factor that has not been addressed to date. By carrying out numerous experiments and computational simulations thereof, we ascertain that the number of rays in a ray system ∝ D/λ, where D is the diameter of the ball and λ is the wavelength of the undulations. Further, we show that the ejecta in a ray system originates in a narrow annulus of diameter D with the center at the site of impact. Our findings may help shed light on the enigmatic ray systems on the Moon and other planetary bodies.
This research was carried out in collaboration with Tapan Sabuwala, Christian Butcher, and Gustavo Gioia.

Collective pattern formations of self-propelled particles are ubiquitous such as flocks of bird, fish school, and bacterial swarming, and it is expected that there exist the unified descriptions of the collective motions. Along this spirit, Vicsek et al. proposed a minimal multi-agent model, which is called the Vicsek model, in 1995. In the Vicsek model, each point particle which has its own moving direction is subject to temporally uncorrelated random directional noise. Each particle aligns to the neighbors, namely only short-range orientational interaction works. Using multi-agent models including the Vicsek model, global directional order in 2D and anomalous density fluctuations, which are called giant number fluctuations, in the ordered phase were predicted in collective motions of self-propelled particles with short-range directional interaction. Indeed, using E. coli elongated with an antibiotic, these two properties were observed in the real system [1].
The particles in the Vicsek model change their direction with no memory. However, there are various kinds of self-propelled particle that keeps its rotation rate for a long time and shows a circular trajectory such as an E. coli close to a wall and a mycoplasma on a glass plate. Using a multi-agent model like the Vicsek model, we elucidated the role of memory of rotation rate. We found that vortices filled the whole area only when the rotation rate of each particle was kept for a while [2].
It is known that microtubules driven by dyneins on a glass plate [3] and C. elegans [4] also have a long memory of rotation rate. Both the self-propelled particles formed many vortices, which are commonly well reproduced by the model in the upper paragraph. This indicates that there exists the unified description of self- propelled particles with memory of rotation rate and short-range directional interaction.
1. D. Nishiguchi, K. H. Nagai, et al., Phys. Rev. E (2017).
2. K. H. Nagai, et al., Phys. Rev. Lett. (2015).
3. Y. Sumino, et al., Nature (2012).
4. T. Sugi, et al., Nat. Commun. (2019).

生命現象の多くは比較的単純な要素の寄せ集めでモデル化できるが、その要素が自発的に動いているために平衡統計力学の枠組みから外れ、おもしろい現象が現れる。たとえば神経幹細胞の培養系はアクティブネマチックであり、向きが揃った状態では流れ場がないが、自発運動の結果の協同現象として、トポロジカル欠陥付近では流れ場が生じうる[1]。今回わたしたちは、ネマチック系で流れが生まれる新しい現象として、細胞の自発運動性とキラリティに依存するエッジカレントを見つけた。本講演では、アクティブネマチック系の簡単なレビューのあと、細胞のキラリティの定量実験と、スタンプ培養環境を使ったエッジカレントの観察を紹介し、数値シミュレーション結果と連続体モデルの解析について議論する。

[1] Kawaguchi, Kageyama, and Sano, Nature 545, 327 (2017).

細菌の細胞質内はタンパク質やRNAなどの高分子によって非常に混み合ってお り、その空間を細胞膜と細胞壁が閉じ込めています。細胞質内の乾燥マス密度 （以下、マス密度）は300 mg/mLにのぼり、この高密度環境が細胞内における 酵素反応などの生体内反応の効率に重要だと考えられています。このように細 胞のマス密度は細胞生理に重要な要素であるにも関わらず、live single-cell での測定が非常に困難であることから、その制御機構についてはほとんど明ら かになっていません。そこで、私たちは枯草菌の細胞をモデルとし、定量位相 顕微鏡の一種であるSpatial light interference microscopy（SLIM）を用い て、live single-cellのマス密度変化を定量しました。その結果、これまでに 予想されていた通り、多くの生育条件において細胞のマス密度は一定に維持さ れていましたが、細胞形態を変化させた場合に限って、細胞のマス密度は非常 にダイナミックに変化していることが分かりました。このことから、体積や表 面積などの細胞形態に関わる変数がマス密度と関係があると考え、現在はその 定式化に取り組んでいます。当日は、これらの定量結果に加え、生物学的な分 子機構にも触れながら、議論させていただきたいと思います。

Stochastic thermodynamics describes the evolution of a system in contact with a thermostat, when fluctuations dominate. This is implicitly assumed to occur most often for micron-scale systems.

We develop experiments at human-scale, i.e. from millimeters to dozen of centimeters. For instance one is based on the principle of Brownian motion, however with a granular gas as heat bath [1]. A core feature is the intrinsic dissipation of this thermostat, that needs to be compensated by a power supply. This bath, in such a Non-Equilibrium Steady State (NESS), seems definitely distinct from a drop of water !

However, our main outcome is that, for all criteria investigated, no qualitative departure could be evidenced by changing the scale or the dissipation : a heuristic use of the Gallavotti-Cohen Fluctuation Theorem and of the Fluctuation-Dissipation Theorem give an ‘effective temperatures’ kT_eff. consistent to within 10% [2] ; the heat flux between two such NESS baths follows the Fourier law on the average [3] ; and the fluctuations of heat flux follows the extended fluctuation theorem (XFT) proposed by Jarzynski et al. in 2004 [4,5].
We explain how kT_eff., defined and mesured in a NESS, exhibits typical value around 10^-6 J, considerably larger than those of molecular systems (kBT~10^-21 J). It however behaves as a unual equilibrium temperature !

At this point, we considered the analogy is validated, as far as stochastic thermodynamics concepts are concerned, and turned to further investigations. We checked that this approach holds in other kinds of NESS baths, such as an elastic plate in wave turbulence regime [6], or large Reynolds number turbulent flow.

We will discuss some woork in progress, and draw some perspectives for this convenient experimental benchtest, in the direction of the relations between energy and information, for instance, but not only.

Références :
[1] Naert A., EuroPhys. Lett. 97 2 (2012) 20010,
[2] J.-Y. Chastaing, J.-C. Géminard and A. Naert,
J. Stat. Mech. 073212 (2017)
[3] Lecomte C.-E. and Naert A., J. Stat. Mech., P11004 (2014),
[4] C. Jarzynski and D. K. Wójcik, Phys. Rev. Lett., vol. 92, p. 230602, Jun 2004.
[5] M. Lamèche, A. Naert, to be published
[6] B. Apffel, A. Naert, S. Aumaître, J. Stat. Mech., vol. 2019, p. 013209, jan 2019

Knits mechanical properties are fundamentally different from those of its constitutive yarn. For instance, a fabric knitted with an inextensible yarn demonstrates a surprising inclination for deformability. Like mechanical systems where geometry plays a preponderant role, such as origami, the mechanical response of knitted fabrics is governed by the pattern imposed on the yarn. In the process of knitting, the yarn is constrained to bend and to cross itself following a periodic pattern, anchoring its topology. The three factors which determine the mechanical response of a knit are the elasticity of the yarn, its topology, and friction between crossing strands. We explored several phenomena that arise from the interplay of these factors, such as the elasticity of a stretched fabric or the fluctuations in the mechanical response revealing an avalanching dynamics.

Close to the onset of an instability, it is expected that fluctuations can play a role. In general, fluctuations act additively (broadly speaking, their effect do not depend on the amplitude of the unstable field) and are responsible for a variety of effects such as the well known anomalous critical exponents of equilibrium phase transition.

In out of equilibrium systems, fluctuations can be multiplicative: their effect vanish when the amplitude of the unstable mode is zero. Several new effects appear. During this seminar I will discuss in particular two topics: what happen to the onset (is it still defined, how to calculate
it)? and what happen above onset (focussing on the so-called on-off intermittent regime).

The presented results will be illustrated with examples in the context of instabilities in fluid dynamics and magneto hydrodynamics.