2015年度セミナー
今年度前期は水曜日午後４時からセミナーを行います。 このセミナーの他にも、毎週火曜日 15時から本郷理学部１号館４４７号室にて行われる統計力学セミナーにも参加しています。
| 日程 | 時間 | 講演者 | タイトル・アブストラクト |
| 3月10日(木) | 13:00 | Dr. Tomotaka Kuwahara (Tohoku Univ.) |
Effective Liouvillian theory in periodically driven open quantum systems
This work explores effective Liouvillian in open quantum systems under periodic driving. The dissipation can induce quantum phenomena which never appear in equilibrium [1], and hence the systematic analysis for such systems has been long desired. The effective Liouvillian in open systems is expected to have similar mathematical structures to those of effective Hamiltonian in closed system. Thus, we can also apply the Floquet-Magnus theory [2,3] in giving the basic formalism for the effective Liouvillian theory. On the other hand, we need a lot of theoretical modifications in applying the basic mathematical tools for closed systems such as the Lieb-Robinson bound [4]. In this seminar, in the light of the above points, I give the fundamental frameworks of the periodic open quantum systems, and show the qualitative difference between the closed and the open systems.
[1] C. K. Chan, T. E. Lee, and S. Gopalakrishnan Phys. Rev. A 91, 051601(R) (2015). |
| 3月10日(木) | 15:00 | Dr. Savannah Garmon (Osaka Pref. Univ.) |
Characteristic dynamics on multiple timescales near two coalescing eigenvalues
Recently the physics of coalescing eigenvalues at an exceptional point (EP) [1, 2] has been studied in a wide variety of physical contexts. When N eigenvalues coalescence at an EPN, the Hamiltonian can no longer be diagonalized but instead can only be reduced to a Jordan block of dimension N. It is reported in the literature that the usual exponential decay is also modified at the exceptional point; however, these studies generally rely on an effective Hamiltonian approach in which the details of the influence of the continuum are washed out. In this study we rely on a formalism [3] that accounts for the continuum in an exact manner to describe the dynamics on multiple timescales in the vicinity of an EP2. In order to report our results we find it necessary to further subdivide the EP2 into the EP2A class and EP2B class [4], in which the EP2A involves the coalescence of two real-valued solutions to create a resonance/anti-resonance pair with complex conjugate eigenvalues while the EP2B involves the coalescence of two resonance eigenvalues to form two new resonances. We find in the vicinity of the EP2B the dynamics follows the expected modified exponential evolution te−Γt for intermediate timescales; however this gives way to a t−3 power law decay for large time scales. Meanwhile the evolution for the EP2A is non-exponential on all timescales, and may be strongly influenced by continuum threshold effects [5].
[1] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1980). |
| 1月28日(木) | 15:00 | 田口真彦氏 （筑波大） |
一次元超伝導システムのモードエンジニアリング
ジョセフソン効果は荷電エネルギーとジョセフソンエネルギーで特徴付けられる。現在、ジョセフソン効果に双対な量子位相滑り(QPS)が電流標準や超伝導ビットなどの応用面からも注目されている。QPSにおいて低温を保ちながら電荷揺らぎを抑えるためには、散逸を起こす抵抗ではなく、インダクタンスが有用である。しかし、ジョセフソン接合などの接合系の近くに大きなインダクタンスを実現することは難しく[1]、近年、超伝導細線やジョセフソン接合列による大きな外部インダクタンスを用いた実験が活発に行われている[2,3,4]。不確定性関係から電荷の揺らぎが押さえられると、位相の揺らぎが支配的になる。[5]により、超伝導ループがジョセフソン接合により閉じられた系において、ループの存在が単一ジョセフソン接合の性質をどのように変えるかが調べられた。そして特に、位相の揺らぎの各モードがジョセフソンエネルギーの繰り込みを引き起こすことが示された。
[1] W. Guichard et al., PRB 81, 064508 (2010). |
| 1月7日(木) | 14:00 | 鈴木貴文氏 （宮下研） |
Photon-assisted current noise through a quantum dot system
Photon-assisted transport through mesoscopic conductors has attracted much attention because the quantum nature of transport processes is significantly modified by photon absorption and emission. The current noise is a useful tool to probe the microscopic processes involved in photon-assisted transport[1]. While much has been known about the noise of noninteracting electrons, the effect of the Coulomb interaction is less well understood. In this study, we develop a systematic scheme to calculate the noise in interacting systems utilizing the Floquet-Green's function method[2]. We derive an explicit expression of the noise within the self-consistent Hartree-Fock approximation, and examine the features of the transport process under a periodically oscillating field.
[1] G. B. Lesovik and L. S. Levitov, Phys. Rev. Lett. 72, 538 (1994) |
| 12月24日(木) | 10:00 | 内山智香子氏 （山梨大） |
環境の影響下でのエネルギー伝送
近年、緑色硫黄細菌をはじめとする光合成細菌の光捕集分子 において、捕集した光エネルギーが９９％の高効率で光合成反 応の中心点に伝送されていることが明らかになってきている。 この光捕集分子に対する4光波混合実験によると、この高効率 なエネルギー伝送には、光エネルギ−伝送を担う色素分子（バク テリオクロロフィル）の周りをとりまいているタンパク質分子によっ て及ぼされる揺らぎの存在が大きな役割を果たしていることが 明らかになってきている[1]。 本セミナーでは、この現象に対する従来の実験、理論両面の 取り組みを紹介する。また、、現在進行形の研究内容についても 触れる予定である。 参考文献：[1] T.Brixner,et.al.,Nature 434, 625 (2005). |
| 12月17日(木) | 14:00 | 富田陽子氏 （芝浦工大） |
ナノコンタクト分子架橋系における過渡電流の研究
近年、半導体量子ドットや分子架橋など、電極に挟まれたナノサイズの微小系を流れる電流の研究が盛んである。これら研究はクーロンブロッケードや近藤効果伝導などの多くの新しい物理を生み出してきたが、そのほとんどは定常電流に関する研究である。このナノコンタクト系を現実のデバイスとして使うためには、短時間のパルス電圧印加などに対する過渡電流の理解が必要となってくる。実際近年、量子ポイント接触において入力パルスが出力では大きく変形される現象がいくつも観測されているが、これを説明するような過渡電流の理論研究がなかった。 そこで、ナノ系を流れる過渡電流を調べるために、密度行列の時間発展方程式（Liouville方程式）に基づき、巨視的な電極の電子分布を射影演算子でグランドカノニカル分布に落とし込む等の操作を行い、ナノコンタクト系の時間発展方程式を導いた。これにより、過渡現象を支配する様々な仕組みが解明できるようになった。例えば、過渡電流は振動しながら定常状態に緩和していくが、振動は電極からナノサイトへの電子の飛び移り確率が振動することで生じ、電極のフェルミエネルギーとナノサイト準位のエネルギー差を反映した量子効果であること、一方緩和は、ナノサイトから電極内の様々な状態に電子がエネルギーを散逸することで生じることを明らかにした。 セミナーでは、これらに加え、ナノ系に電子間相互作用が働く場合や、複数サイトある場合について議論すると共に、最近の発展についても紹介したい。 |
| 12月10日(木) | 14:00 | Prof. Bhabani Prasad Mandal （Banaras Hindu University） |
Introduction to non-Hermitian Quantum Theories
In this talk I will give a long introduction of PT symmetric non-Hermitian theories and discuss few applications of such theories. I will explain how one can systematically obtain a consistent quantum theory with with non-Hermitian system with unbroken PT symmetry. Further I will discuss how such a complex extension is useful in various branches of physics. |
| 12月3日(木) | 14:00 | 伊藤 創祐氏 （東工大） |
シグナル伝達における正確性-熱散逸のトレードオフと情報熱力学
生体内では様々な化学反応の連鎖により、シグナル伝達と呼ばれる情報伝達が行われており、生命の維持における重要な役割を果たしている。 このシグナル伝達を、近年発展してきた確率的な熱力学(stochastic thermodynamics)を用いて解析する試みが行われている。 中でも情報伝達の正確性と熱散逸のトレードオフ関係[1-3]が特に注目を浴びており、様々な観点から生体内の情報通信における熱力学の重要性が調べられてきている。 我々はこれに関連して、Maxwellのデーモンの理論による確率的な熱力学の拡張として発展してきた情報熱力学を用いて、 単純な2系Langevin系で熱散逸と情報伝達の正確性のトレードオフを示し、情報熱力学とShannonの通信路符号化定理との間にアナロジーが成り立つことを指摘した[4]。 今回のセミナーでは情報熱力学の最近の進展を紹介しつつ、Shannonの通信路符号化定理とのアナロジーがより一般的な設定に拡張可能であることを説明したい。
[1] G. Lan, P. Sartori, S. Neumann, V. Sourjik and Y. Tu, Nature Phys. 8, 422-428 (2012). |
| 11月26日(木) | 14:00 | 富田 裕介 氏 （芝浦工大） |
平衡緩和過程による秩序相の分類
相転移・臨界現象を理解する一つの手立てとして、臨界指数を精度良く、もしくは厳密に求め、系の普遍クラスを明らかにする方法が広く用いられている。この方法は、種々多様な臨界現象を普遍クラスで分類し、臨界現象を理解するための見通しの良い枠組みを与えたが、臨界点以下の秩序相のダイナミクスに関する情報は含んでいない。 今、興味の対象となっている多くの系は、フラストレーションやランダムネスによる遅い緩和を見せる系であり、その点で、従来的な解析手法は問題の本質的理解を外したものとなっている。本講演では、1次元長距離相互作用Ising模型を例に取り、平衡状態における緩和過程(自己相関関数)の振る舞いによって秩序相を分類するアプローチ方法を提案する。この分類方法は、秩序相のダイナミクスに対する直接的な情報を与えるものであり、また秩序形成に対するより深い理解と材料物質の開発という、基礎・応用の両面で重要な論点となり得るものであることを示す。 |
| 11月19日(木) | 14:00 | 金澤 輝代士 氏 （東工大） |
Asymptotic derivation of the non-Gaussian Langevin equation and its analytical solution
Fluctuation in small systems has attracted wide interest because of the recent experimental development in biological, colloidal, and electrical systems. As accurate data on fluctuation have become accessible, the importance of mathematical modeling of fluctuation’s dynamics has been increasing. One of the minimal models for such systems is the Langevin equation, which is a simple model composed of the viscous friction and the white Gaussian noise. The validity of the Langevin model has been shown in terms of some microscopic theories [1], and this model has been used not only theoretically but also experimentally in describing thermal fluctuation. On the other hand, non-Gaussian properties of fluctuation are reported to emerge in athermal systems, such as biological, granular, and electrical systems. A natural question then would arises: When and how does the non-Gaussian fluctuation emerge for athermal systems? In this seminar, we present a systematic method to derive a Langevin-like equation driven by non-Gaussian noise for a wide class of stochastic athermal systems, starting from master equations and developing an asymptotic expansion [2, 3]. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. We also derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. Furthermore, we obtain the full-order asymptotic formula of the steady distribution function for an arbitrary strong non-linear friction, and show that the first-order approximation corresponds to the independent kick model [4]. We apply our formulation to a granular motor under viscous and Coulombic frictions, and analytically obtain the angular velocity distribution functions. Our theory demonstrates that the non-Gaussian Langevin equation is a minimal model of athermal systems. [1] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland (2007). [2] K. Kanazawa, T.G. Sano, T. Sagawa, and H. Hayakawa, Phys. Rev. Lett. 114, 090601 (2015). [3] K. Kanazawa, T.G. Sano, T. Sagawa, and H. Hayakawa, J. Stat. Phys. 160, 1294 (2015). [4] J. Talbot, R.D. Wildman, and P. Viot, Phys. Rev. Lett. 107, 138001 (2011). |
| 11月13日(金) | 14:30 | Amnon Aharony 氏 (Ben Gurion University, Tel Aviv University) |
Spin-splitting through nano-scale devices
Quantum computing requires the ability to write and read quantum information on the spinors of electrons. Here we consider mobile electrons, which move through mesoscopic (or molecular) quantum networks. Figure (a) below shows a simple interferometer. Combining spin-orbit interactions, whose strength can be tuned by external gate voltages, and the Aharonov-Bohm flux, which can be tuned by an external magnetic field, one can generate full spin filtering which is independent on the electron energy: the outgoing electrons are polarized along a desired direction. Given a beam of polarized electrons, the charge conductance of the same network depends on their polarization, allowing 'reading' the qubit information. [1] Leakage of electrons through side branches, or dephasing, break time-reversal symmetry, and can yield full filtering without a magnetic flux. [2] At a given electron energy, filtering can be achieved by tuning two gate voltages. [3] Filtering can also be achieved for a single one dimensional chain which has spin-orbit interactions, when the chain vibrates in the transverse direction. [4] Transient time-dependent polarizations can be generated even without a magnetic flux. [5] Many recent experiments exhibit spin splitting through organic helical molecules. Using a simple tight-binding model [Fig. (b) below], we also show that spin-orbit interactions plus leakage can generate such splitting. [1] A. Aharony, Y. Tokura, G. Z. Cohen, O. Entin-Wohlman, and S. Katsumoto, Phys. Rev. B 84, 035323 (2011). [2] S. Matityahu, A. Aharony, O. Entin-Wohlman and S. Katsumoto, Phys. Rev. B 87, 205438 (2013). [3] S. Matityahu, A. Aharony, O. Entin-Wohlman, and S. Tarucha, New J. Phys. 15, 125017 (2013). [4] R. I. Shekhter, O. Entin-Wohlman, and A. Aharony, Phys. Rev. Lett. 111, 176602 (2013); Phys. Rev. B 90, 045401 (2014). [5] M. Wei-Yuan Tu, A. Aharony, W-M Zhang and O. Entin-Wohlman, Phys. Rev. B 90, 165422 (2014). |
| 11月12日(木) | 14:00 | Ora Entin-Wohlman 氏 (Ben Gurion University, Tel Aviv University) |
Thermoelectric Transport in Nanoscale Junctions
Heat and charge currents through junctions bridging two electronic baths (of possibly different temperatures and different chemical potentials), and coupled to a third thermal electrode are considered [figure (a) below]. The role of inelastic processes between the charge carriers and the thermal terminal is emphasized. In particular, the efficiency and the coefficient of performance are analyzed. Two procedures are analyzed. (a) One of the electronic terminals is cooled by investing thermal power (from the thermal bath) and electric power (from voltage applied across the electronic junction); (b) The invested thermal power from the boson bath is exploited to cool one electronic terminal and to produce electric power. Rather surprisingly, the coefficient of performance of (b) can be enhanced as compared to that of (a).[1-3] We also analize the thermoelectric transport through a ring threaded by an Aharonov-Bohm flux, with a molecular bridge on one of its arms [figure (b) below]. The transport electrons interact with the vibrational excitations of that molecule. This nano-system is connected to three terminals: two are electronic reservoirs, which supply the transport electrons, and the third is the phonon bath which thermalizes the molecular vibrations. Expressions for the transport coefficients, relating all charge and heat currents to the temperature and chemical potential differences between the terminals, are derived to second order in the electron-vibration coupling. At linear response, all these coefficients obey the full Onsager-Casimir relations. When the phonon bath is held at a temperature different from those of the electronic reservoirs, a heat current exchanged between the molecular vibrations and the transport electrons can be converted into electric and/or heat electrons' currents. The related transport coefficients, which exist only due to the electron-vibration coupling, change sign under the interchange between the electronic terminals and the sign change of the magnetic flux. It is also demonstrated that the Aharonov-Bohm flux can enhance this type of conversion.[4] [1]O. Entin-Wohlman, Y. Imry, and A. Aharony, Phys. Rev. B 91, 054302 (2015). [2] O. Entin-Wohlman, J-H. Jiang, and Y. Imry, Phys. Rev. E 89, 012123 (2014). [3] J-H. Jiang, O. Entin-Wohlman, and Y. Imry, New J. Phys. 15, 075021 (2013). [4] O. Entin-Wohlman and A.Phys. Rev. B 85, 085401 (2012). |
| 10月29日(木) | 14:00 | Eva-Maria Graefe 氏 (Imperial College London) |
Mean-field and many-particle correspondence for a quantum atom-molecule conversion system
There is currently considerable interest in experiments with Bose-Einstein condensates (BECs) of cold atoms that can associate to form multi-atomic molecules and vice versa. A full theoretical description of cold atoms and BECs requires modelling of many-particle quantum dynamics, which quickly goes beyond the scope of computational accessibility for realistic setups. For low densities, large particle numbers, and short times, a BEC can be effectively described by a single macroscopic wave function. This mean-field approximation is closely related to the classical limit of single particle physics. Thus, semiclassical methods can be applied to model many-particle features on top of the mean-field description. Here we consider the simplest example system of an atom-molecule conversion system where atoms can combine into two-atomic molecules, and only one basis state is considered for atoms and molecules respectively. The many-particle system can be described by a deformed SU(2) algebra, and the mean-field dynamics is confined to a teardrop shape that replaces the Bloch sphere of a conventional two-mode system. We introduce a semiclassical quantisation condition and demonstrate that the many-particle spectrum can be accurately recovered from the mean-field dynamics. This allows us to derive an analytic expression for the many-particle density of states in the semiclassical limit of large particle numbers, which shows a divergence typical of a quantum-phase transition. |
| 10月22日(木) | 14:00 | 桑原知剛 氏 (東大理) |
有限時間スケールにおける時間周期系の一般理論
本研究では周期的な駆動が掛かった量子多体系の動的構造を理解することを目的とする。このような時間周期系は、システムの構造を制御するFloquet engineeringという分野の発展と共に新しいブレイクスルーを起こしうる物理系として注目を集めている。一方で、時間周期系の定常状態に関する十分な理解は極限的な場合 (相互作用しないフェルミオン系や高周波極限) を除いて得られていない。一般的な理論として、このような理想極限が少しでも外れると定常状態は熱化現象のため興味深い性質を示さなくなることが知られている。ところが、実用的には時間周期系の無限時間極限を見ることは無意味で、実験の時間スケールで見えるような現象に興味がある。このような有限時間スケールで系の動的構造を理解することが今後の応用上極めて重要であるにも関わらず、厳密な解析はほとんどなされていないのが現状である。我々はFloquet-Magnus 理論をベースとして、有限時間ダイナミクスの基本的な枠組みを与える。 |
| 4月16日(木) | 14:00 | 森 貴司 氏 (東大理) |
Long-time behavior of a quantum system subject to periodic driving |
| 4月23日(木) | 14:00 | 辻 直人 氏 (理研) |
Title: Higgs mode in superconductors Abstract: Higgs mode is a collective amplitude mode of the order parameter in a spontaneous symmetry broken phase. After reviewing the Higgs physics in condensed matter systems, I present our recent work on an experimental and theoretical finding of a resonance phenomenon between the Higgs mode and electromagnetic fields in superconductors. |
| 4月30日(木) | 14:00 | 川本 達郎 氏 (東工大) |
Title: Spectral method of graph partitioning and localization of eigenvectors Abstract: Spectral method is a popular heuristics for discrete optimization problem and it is often used in graph partitioning. In spectral method, one solves for the eigenvector which is expected to have the information of modules and partitions the graph according to the sign of its components. When a localized eigenvector takes place, however, the standard spectral method fails to identify the modules. We investigate numerically and analytically, when the localization of eigenvectors appear in graph partitioning problems. |
| 5月7日(木) | 14:00 | 今村 卓史 氏 (千葉大) |
Title: Determinantal structures in the O'Connell-Yor polymer model Abstract: The O'Connell-Yor polymer model is a directed polymer model in random media in two (one discrete and one continuous) dimensions. Because of its rich mathematical structures, it has been playing a central role in the recent developments in the Kardar-Parisi-Zhang universality class. In this talk, we give a simple representation for the moment generating function of the polymer partition function in terms of a determinantal measure. This measure can be regarded as an extension of the probability measure of the eigenvalues for the Gaussian unitary ensemble (GUE) in random matrix theory. For establishing the representation, we clarify some underlying determinantal structures in the O'Connell-Yor model. |
| 5月14日(木) | 14:00 | 佐藤 純 氏 (先端研) |
Title: Introduction to Bethe ansatz Abstract: Bethe ansatz is a well-known method to obtain exact eigenvalues and eigenvectors of 1d quantum systems. I will give a brief introduction to coordinate Bethe asnatz taking 1d Bose gas as a simple example. The lecture will be given via a white board and audiences are required to follow all the equations by their own hand. |
| 5月21日(木) | 14:00 | 小渕 智之 氏 (東工大) |
Title: Properties of probability distributions constrained by observables: Implication to maximum entropy modeling' Abstract: Stochastic inverse problem is to construct a probability distribution based on some given data on certain observables of a target system. The inferred probability distribution is expected to well approximate the target probability distribution precisely describing the target system. Usually due to the curse of dimensionality, the given data is not enough to uniquely determine the probability distribution, thus there are many possible distributions which reproduce the data. We invent a formulation to analyze such many probability distributions constrained by observables. The formulation, based on technicalities of random spin systems, introduces a new probability measure on the possible probability distributions, which enables us to study several quantitative relations such as the one between the number of given data and the distance of typical inferred distributions from the target one. This formulation allows us to treat several different situations in an unified manner, and we focus on the role of the maximum entropy principle by using this flexibility. In this talk, I explain the formulation and the analytical solution in an ideal case. Some implications to more realistic cases will be also presented. This work is in collaboration with Prof. Monasson and Cocco in Ecole Normale Superieure. |
| 5月28日(木) | 14:00 | 白井達彦 氏
(東大理) |
Title: 時間周期的な外場の掛かった共振器系で起こる新奇な動的相転移現象について Abstract: 時間周期的な外場の掛かった共振器系の定常状態で起こる協力現象について報 告する。共振器系では光と物質との間の相互作用を起源として、様々な協力現 象が現れ、またレーザーによって非平衡状態を実現することが可能である。最 近では実験技術の進歩に伴い、相互作用の強い領域が実現可能となっている。 本発表では、その相互作用の強い領域で新たに見出された、駆動外場が本質的 な役割を担って現れる相転移現象について報告する[1]。 一方で、時間周期的な外場の掛かった量子開放系の定常状態では、平衡状態と は異なり詳細釣合の関係が成り立たず、そのため定常状態は熱浴の種類や熱浴 との相互作用に依存する[2]。ここでは、そういった熱浴の詳細に依存せずに定 常状態を記述するための条件について考え[3]、今回明らかとなった非平衡相転 移現象が、その条件の下で、どのように記述されるかについて報告する。 [1] T. Shirai, T. Mori, and S. Miyashita, J. Phys. B: At. Mol. Opt. Phys. 47, 025501(2014). [2] W. Kohn, J. Stat. Phys 103, 417 (2001). [3] T. Shirai, T. Mori, and S. Miyashita, Phys. Rev. E 91, 030101(R) (2015). |
| 6月4日(木) | 14:00 | 高吉 慎太郎 氏
(東大理) |
title: Symmetry protected topological phase in quantum spin systems abstract: A symmetry protected topological (SPT) phase is a short-range entangled state that cannot be continuously deformed into a trivial state only if some symmetry is imposed to the system. In this seminar, I will first give a brief explanation of the basic properties of the SPT phase taking Haldane phase (ground state of S=1 Heisenberg antiferromagnets) as an example. Next, I show that magnetization plateau states of one-dimensional antiferromagnets in external magnetic field can be considered as an SPT phase when S-m is odd, where S and m represent a spin quantum number and magnetization per site, respectively, if the system respects a link-center inversion symmetry. I use a mapping into field theories of a nonlinear sigma model with a Berry phase term and see the structure of ground state wave function obtained by a path integral approach dictates whether or not the system is in the SPT phase. We further verify this prediction through numerical calculations of the entanglement spectra and an analysis by a matrix product state representation. |
| 6月11日(木) | 14:00 | Gonzalo Ordonez 氏
(Butler University) |
Title: Dynamical breaking of time-reversal symmetry in open quantum systems
Abstract: We consider a class of open quantum systems modeled by a tight-binding Hamiltonian. We start with a time-symmetric expansion of unity involving discrete eigenstates of the Hamiltonian. This expansion includes both resonant and anti-resonant states. We show how time-reversal symmetry is broken dynamically as an initially time-reversal symmetric state evolves in time. We show that there is a time-scale for the breaking of time-reversal symmetry, associated with the Zeno time. We also compare the time symmetric expansion with a time-asymmetric expansion used previously by several researchers including the first author. We show how the time-symmetric expansion bypasses the non-Hilbert nature of the resonant and anti-resonant states, which previously introduced divergences into the time-asymmetric expansion. |
| 6月25日(木) | 14:00 | 上田 宏 氏
(明治大) |
Title: Corner transfer matrix and tensor renormalization group Abstract: The Baxter’s corner transfer matrix (CTM) is a powerful tool for analytical/numerical study of statistical models in two dimension (2D). Through the well-known quantum-classical correspondence, spectra of CTM is relevant to Schmidt coefficients in the Schmidt decomposition of ground states in 1D quantum systems. The tensor renormalization group (TRG) and a variant of it (HOTRG) are also useful numerical tools for analysis of classical 2D systems. In this seminar, I will show that coarse-grained tensors of TRG methods are characterized by the doubling of spectrum of CTM. Then, I will introduce recent progress of tensor network methods. |
| 7月2日(木) | 14:00 | 中村統太 氏
(芝浦工大) |
Title:
From measurements to inferences of physical quantities in numerical simulations Abstract: Measurements of a physical quantity in numerical simulations have been made independently at each step using a definition formula. We expand this scheme to a most-probable inference using raw big data. A physical quantity at each step is inferred simultaneously and cooperatively using a scaling hypothesis. High-precision estimates become possible. We demonstrate the method in the three-dimensional Heisenberg spin-glass model. The dynamic correlation length, xi(t), is obtained from relaxation data of the correlation function, f(r; t) [r: distance, t: time] using a scaling ansatz: f(r,t) \sim xi(t)^{-1-eta}F(r/xi(t)). A dynamic-correlation-length scaling analysis suggests that the spin- glass and the chiral-glass transition occur at the same temperature with a common exponent nu. |
| 7月9日(木) | 14:00 | 森本 高裕 氏
(理研) |
Title：Topological charges of three-dimensional Dirac semimetals with
rotation symmetry Abstract： Weyl semimetals are three-dimensional (3D) analogs of graphene and have gapless low-energy excitations of Weyl fermions around the stable gapless points called the Weyl points. Weyl semimetal are realized when either of time-reversal symmetry or inversion symmetry is broken. The stability of Weyl points has a topological origin; Weyl points are monopoles in the momentum space which are sources or drains of effective magnetic fields in the momentum space (the Berry curvature) and are assigned with integer topological charges defined by an integral of the Berry curvature. Weyl semimetals support anomalous transport properties due to the stable gapless excitations. Recently, the discovery of 3D Dirac semimetals in Na3Bi and Cd3As2 demonstrates that a Dirac point with four-fold degeneracy can also be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na3Bi and Cd3As2 have not been clarified yet. In this talk, I will review the topological characterization of 3D Weyl semimetals. Then I will show that topological charges for Dirac semimetals Na3Bi and Cd3As2 can be defined by considering the rotation symmetry along with time-reversal and inversion symmetries. I will also discuss novel Dirac semimetals protected by nonsymmorphic screw rotation symmetry. [1] B-J. Yang, T. Morimoto, A. Furusaki, arXiv: 1506.01548 |
| 7月23日(木) | 14:00 | Fabio Bagarello 氏
(Univ. of Palermo) |
Title: time evolutions and probability transitions for non
self-adjoint Hamiltonians Abstract: After a general introduction to the functional structure of pseudo-bosons and pseudo-fermions, we propose different inequivalent definitions of probability transitions for systems driven by non self-adjoint Hamiltonians. In this context, we will discuss some examples arising from pseudo-bosons and pseudo-fermions. |
| 7月24日(金) | 14:00 | Masanori Shimono 氏
(Univ. of Palermo) |
Title:
Multiple scale networks in the brain
Abstract: Brain is certainly one of the most complex, well-organized, systems. Recently, neuroscientists are acquiring newly found abilities to observe widely at various scale organizations of the brain. However, even if we could accumulate huge data, neuroscientists face difficulty of how we could extract rules existing behind of the complex data. This presentation includes two parts: The first half presents how global brain networks relate with properties at individual brain regions, especially, densities of cells. Distribution of cells provides a vantage point to connect individual brain regions with local circuits of cells. The second half presents a study zooming into the organization of local neuronal circuits within a brain region. In the first study, global brain networks were defined as fiber pathways connecting brain regions. Briefly speaking, one new trend was found: Neuron density is sparser at associate regions, where are regions connected with many different network modules (such as visual, auditory, motor modules) widely (Shimono, 2013). This trend indicated that a small number of neurons are enrolled for integration or for distributing information of different modules. Because the small number of neurons, we can expect the information run through the brain by short path lengths and by high efficiency (Sporns, 2013). In the second study, we recorded neuronal data using a Multi-Electrode Array (MEA) system, which makes it possible to record from up to 600 neurons in 1-2mm2 brain regions. Surprisingly, the reconstructed effective connectivity between neurons showed similar topological properties with previous patch clamp experiments (Perins et al., 2011). This result indicated that the effective connectivity reflects underlying synaptic interactions. Furthermore, we could firstly quantify and visualize multiple scale non-uniform organizations, as shown as hubs, clusters, and modules (communities) of neuronal networks (Shimono, Beggs, 2014). In summary, the brain network demonstrates unique non-uniform and multiple scale organizations from global macroscopic scale to microscopic scale. Based on idea of multiple scale organizations, and in comparisons and integrations of different scale data on the same computational framework, we will be able to reach a much deeper understanding of how brains are designed for satisfying functional demands than current understandings provided merely from one spato-temporal scale or from a single recording method. |