統計力学セミナー予定表 2015年度


連絡先: 島田尚(shimadaあっと ap.t.u-tokyo.ac.jp)、 森貴司(moriあっと spin.phys.s.u-tokyo.ac.jp)
宮下研究室伊藤研究室 (セミナー)| 羽田野研究室 (セミナー)

これからのセミナー

日時 場所 講演者(敬称略) 講演題目

これまでのセミナー

日時 講演者(敬称略) 講演題目
1月19日15時 橋本一成(山梨大学) Complex spectrum of Liouvillian and transport process in 1D quantum perfect Lorentz gas
12月15日15時 赤城裕 Topological defects in quantum spin-nematics
12月8日15時 川本達郎(東京工業大学) Unifying framework of graph partitioning and its statistical mechanical analysis
12月1日15時 田島裕康(理化学研究所) Measurement-based Formulation of Quantum Heat Engine and Optimal Efficiency with Finite-Size Effect
11月24日15時 羽田野直道 Two methods of computing the inverse localization length in one dimension
10月27日15時 太田卓見(京都大学基礎物理学研究所) Topological and Dynamical Properties of Majorana Fermions in One Dimension
10月20日15時 諏訪秀麿 Generalized Moment Method for Gap Estimation and Application to Deconfined Criticality
10月13日15時 森貴司 Generic long-time behavior of periodically driven quantum systems in high-frequency regime
9月15日13時30分 Roy Chantrell(University of York) multi scale approaches to magnetic materials modelling
8月21日13時 George Sudarshan(Center for Complex Quantum Systems, University of Texas at Austin, Austin, Texas, USA) Quantum Zeno Effect
7月21日15時 Fabio Bagarello(DEIM, Universit di Palermo, Viale delle Scienze) a mathematical model of alliances in politics
7月14日15時 安田勇輝(東京大学大学院理学系研究科 地球惑星科学専攻) An investigation on an atmospheric phenomenon "Stratospheric Sudden Warming" in terms of equilibrium statistical mechanics
7月7日15時 島田尚 An “Ising model” of open and evolving systems
6月30日15時 Cristian Enachescu(Alexandru Ioan Cuza University) Cluster growth in various 2D and 3D shapes of spin crossover compounds in the framework of elastic models
6月23日15時 桂法称 Exact ground states and topological order in interacting Kitaev chains
6月16日15時 Gonzalo Ordonez(Department of Physics and Astronomy, Butler University) Impurity-Controlled Transport within a Finite Disordered Lattice
6月9日15時 Per Arne Rikvold(Florida State University) Phase Diagrams for an Ising Model with Competing Short-range Antiferromagnetic and Long-range Ferromagnetic Interactions
6月2日15時 藤堂眞治 Tensor Network Algorithm for 2D Frustrated Magnets
5月26日15時 Ferenc Kun(University of Debrecen) Fracture and fragmentation of heterogeneous materials under compression
5月19日15時 伊藤伸泰 Factors of urban traffic
5月12日15時 桑原知剛 Universal character of metastability in periodically driven systems
4月28日15時 羽田野直道 Analytic calculation of non-adiabatic dynamicsaround an exceptional point
4月21日15時 福島孝治(東京大学大学院総合文化研究科) Random first-order transition of a spin-glass model in three dimensions
4月14日15時 宮下精二 Effects of elastic interactions on phase transitions of systems with various types of short range interactions
4月7日15時 新M1 研究紹介
所属が書かれていない講演者は、宮下研、伊藤研、藤堂研、羽田野研、桂研の所属です。
過去のセミナー: 2014年度2013年度2012年度2011年度2010年度2009年度2008年度2007年度2006年度2005年度2004年度2003年度2002年度2001年度2000年度1999年度

第25回

日時:1月19日15時より

場所:理学部1号館4階447号室

講演者:橋本一成(山梨大学)

講演タイトル:Complex spectrum of Liouvillian and transport process in 1D quantum perfect Lorentz gas

講演要旨:
Transport processes in a one-dimensional (1D) quantum perfect Lorentz gas is discussed based on the complex spectral represe ntation of the Liouville-von Neumann equation. Complex spectrum of the Liouville-von Newmann operator (Liouvillian) is derived by applying the Brillouin-Wigner-Feshbach fo rmalism to the Liouville-von Neumann equation. In hydrodynamic regime, where spatial inhomogeneity of particle distribution is much larger than mean-free-length, it is wel l-known that imaginary part of the spectrum gives several transport coefficients such as diffusion coefficient, and it has b een studied extensively. On the other hand, its structure in non-hydrodynamic regime has been poorly understood. In this talk, I will discuss structure of the complex spectrum of the system in the non-hydrodynamic regime. There I will show that the spectrum has several non-trivial structures such as exceptional points (EPs) or a structure refle cting microscopic form of the interaction potential between particles. As a physical effect of the spectral structures, I will show that the EPs in the spectrum of the Liouvillian lead to telegra ph equation for the spatial time development of the Wigner distribution function of the test particle.

第24回

日時:12月15日15時より

場所:理学部1号館4階447号室

講演者:赤城裕

講演タイトル:Topological defects in quantum spin-nematics

講演要旨:
Topological defects play an important role in the theory of nematic phases in liquid crystals. However, relatively little is known about their role in quantum spin nematic phases which have no long-range dipole order and break only spin-rotational symmetry [1-4]. Here, we consider the topological defects in these nontrivial states. The model is the spin-1 bilinear biqua dratic model on the triangular lattice [5-7]. Using homotopy analysis and numerical optimization approach, simulated anneali ng, we identify a new family of solitons at a particular point in parameter space, in which the system has global SU(3) symm etry. We also find that wave functions with higher topological charges spontaneously decay into “elementary” solitons with emergent interactions. This result suggests that it could be possible to realize a new class of interacting soliton [8,9].

[1] B. A. Ivanov, R. S. Khymyn, and A. K. Kolezhuk, Phys. Rev. Lett. 100, 047203 (2008).
[2] T. Grover and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011).
[3] J. Takano and H. Tsunetsugu, J. Phys. Soc. Jpn. 80, 094707 (2011).
[4] C. Xu and A. W. W. Ludwig, Phys. Rev. Lett, 108, 047202 (2012).
[5] A. Lauchil, F. Mila, and K. Penc, Phys. Rev. Lett. 97, 087205 (2006).
[6] H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006).
[7] A. Smerald and N. Shannon, Phys. Rev. B 88, 184430 (2013).
[8] H. T. Ueda, Y. Akagi, and N. Shannon, preprint (arXiv:1511.06515).
[9] Y. Akagi, H. T. Ueda, and N. Shannon, in preparation.

第23回

日時:12月8日15時より

場所:理学部1号館4階447号室

講演者:川本達郎(東京工業大学)

講演タイトル:Unifying framework of graph partitioning and its statistical mechanical analysis

講演要旨:
We show that modularity maximization with the resolution parameter offers a unifying framework of graph partitioning. In this framework, we demonstrate that the spectral method exhibits universal detectability, irrespective of the value of the resolution parameter, as long as the graph is partitioned. Furthermore, we show that when the resolution parameter is sufficiently small, a first-order phase transition occurs, resulting in the graph being unpartitioned.

reference:
http://arxiv.org/abs/1509.06484

第22回

日時:12月1日15時より

場所:理学部1号館4階447号室

講演者:田島裕康(理化学研究所)

講演タイトル:Measurement-based Formulation of Quantum Heat Engine and Optimal Efficiency with Finite-Size Effect

講演要旨:
Today, theoretic analysis about quantum-scale heat engines is achieving a splendid success. They clarify that the average pe rformance of these small-size heat engines obeys the second law of the macroscopic thermodynamics[1,2], and that the single- shot performance of the heat engines obeys different rules[3,4]. They also clarifies the thermodynamic laws for information processing [5,6].

In spite of these success, there are still two unsolved problems for constructing the thermodynamics of small-size systems. First, the above researches formulate the quantum heat engine in various ways, and the relationship among the formulations h as not been sufficiently discussed. Second, The above statistical mechanical approches have never treated the finite-size he at baths. On the other hand, the macroscopic thermodynamics can treat macroscopic finite-size baths. It gives the optimal bo unds of the performance of the heat engines with arbitrary-size baths whenever the baths are macroscopic. However, what is t he quantitative definition of "macroscopic system"?

In this talk, we give two results which shed a light on those two problems. Firstly, we classify the previous formulations of quantum heat engines, and derive a trade-off relation that clarifies a pro blem of a widely-used formulation of quantum heat engine controlled by a classical controller, in which the time evolution o f the internal system (working body and heat baths) is formulated as a unitary transformation. In order to dissolve this problem, we remodel a quantum heat engine controlled by a classical controller as a general measur ement process. Our measurement-based formulation is consistent with the Fully Quantum formulation, which is another widely- used formulation of quantum heat engine.

Second, we derive the optimal efficiency of quantum (or classical) heat engines whose heat baths are $n$-particle systems. W e give the optimal work extraction process as an energy-preserving unitary time evolution among the heat baths and the work storage. During the unitary, the entropy gain of the work storage is so negligibly small as compared with the energy gain of the work storage, i.e., we can interpret the energy gain as the extracted work. With using our results, we evaluate the accuracy of the macroscopic thermodynamics for the heat engines with finite-size hea t baths from the statistical mechanical viewpoint.

The details of the contents in this talk are in the articles arXiv:1504.06150.v2 and arXiv:1405.6457.v2, which are collaborations with Prof. Masahito Hayashi at Nagoya University.

References:
[1] H. Tasaki, arXiv:cond-mat/0009244 (2000).
[2] P. Skrzypczyk, A. J. Short and P. Sandu, Nature Communications 5, 4185, (2014)
[3] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
[4] F. G. S. L. Brandao, M. Horodeck, N. H. Y. Ng, J. Oppenheim, and S. Wehner, PNAS, 112,3215(2015).
[5] T. Sagawa, M. Ueda, Phys. Rev. Lett. 102 250602 (2009).
[6] L. Rio, J. Aberg, R. Renner, O. Dahlsten, and V. Vedral, Nature,474, 61, (2011).

第21回

日時:11月24日15時より

場所:理学部1号館4階447号室

講演者:羽田野直道

講演タイトル:Two methods of computing the inverse localization length in one dimension

講演要旨:
I will present two independent methods that I have found to compute numerically the inverse localization length (the Lyapuno v exponent) of the one-dimensional random Anderson model. They indeed give consistent results for the random-potential model.

I proposed the first method as a by-product of studying the spectrum of the non-Hermitian random Anderson model [1], in whic h an imaginary vector potential gives the non-Hermiticity. We obtain the inverse localization length of the Hermitian model as the edges of the bubble of the complex spectrum of the non-Hermitian model.

The second method is the kernel-polynomial expansion [2] of the inverse localization length. I transform the Chebyshev-polyn omial expansion of the density of states [3] to that of the localization length, using the Thouless formula [4]. The expansi on produces a smoother dataset than the expansion of the density of states because the expansion coefficients become smaller in high orders.

I then extend the two methods to non-Hermitian matrices [5]. I use a random-sign model [6] as an example. I first introduce the imaginary vector potential to the random-sign model [7] to obtain the contours of the inverse localization length in the complex eigenvalue plane. I then combine the method of Hermitization [8] with a generalized Thouless relation [9] to obtain the Chebyshev polynomial expansion of the inverse localization length of non-Hermitian matrices.

[1] N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996); Phys. Rev. B 56, 8651 (1997).
[2] A. Weiss e, G. Wellein, A. Alvermann and H. Fehske, Rev. Mod. Phys. 78, 275 (2006).
[3] R.N. Silver and H. Roeder, Int. J. Mod. Phys. C 5, 735 (1994);
R.N. Silver, H. Roeder, A.F. Voter and J.D. Kress, J. Comp. Phys. 124, 115 (1996);
R.N. Silver and H. Roeder, Phys. Rev. E 56, 4822 (1997).
[4] D.J. Thouless, J. Phys. C 5, 77 (1972);
[5] N. Hatano and J. Feinberg, in preparation.
[6] J. Feinberg and A. Zee, Phys. Rev. E 59, 6433 (1999)
[7] A. Amir, N. Hatano and D.R. Nelson, in preparation.
[8] J. Feinberg and A. Zee, Nucl. Phys. B 504 [FS] (1997) 579
[9] B. Derrida, J.L. Jacobsen and R. Zeitak, J. Stat. Phys. 98, 31 (2000)

第20回

日時:10月27日15時より

場所:理学部1号館4階447号室

講演者:太田卓見(京都大学基礎物理学研究所)

講演タイトル:Topological and Dynamical Properties of Majorana Fermions in One Dimension

講演要旨:
Recently, motivated by condensed matter physics and quantum information science, topological phases have attracted both theoretical and experimental attention. In the phases, dynamics of edge modes depends on the topological properties of the system. In this talk, we study the static and dynamical properties of Majorana fermions in one dimension. First, we investigate the quantum phase transitions of a generalized cluster model [1], which shows variety of topological phases. We characterize each phase by the entanglement spectrum (ES) and the string correlation functions (SCFs). Second, we study the dynamical properties during an interaction sweep across the critical points associated with topological phases. For slow sweep, spatially periodic and oscillating structures are found both in the ES and in the SCFs. These structures are understood in terms of the Bogoliubov excitations generated near the critical points. This breakdown of adiabaticity is due to the topological degeneracy.

Reference
[1] T. Ohta, S. Tanaka, I. Danshita, and K. Totsuka, J. Phys. Soc. Jpn. 84, 063001 (2015). (arXiv:1503.03204)

第19回

日時:10月20日15時より

場所:理学部1号館4階447号室

講演者:諏訪秀麿

講演タイトル:Generalized Moment Method for Gap Estimation and Application to Deconfined Criticality

講演要旨:
We have formulated a convergent sequence for the energy gap estimation in the worldline quantum Monte Carlo method[1]. The ambiguity left in the conventional gap calculation for quantum systems is eliminated. In the meantime, the deconfined criticality phenomena[2] has caught a great deal of attention recently; the non-trivial criticality accompanied by deconfined spinons will appear between two ordered phases, e.g., the Neel phase and the valence-bond solid phase, which should be a discontinuous phase transition according to the Landau-Ginsburg-Wilson paradigm. We simulated the phase transition of the SU(2) J-Q model[3] and estimated the transition point by the excitation-gap analysis. At the transition point, we found an unconventional gapless sector that should appear if the phase transition is continuous. The debate of the deconfined criticality and our results will be explained after the methodology of our approach to gap estimation.

[1] H. Suwa and S. Todo Phys. Rev. Lett. 115, 080601 (2015).
[2] Senthil et al Science 303, 1490 (2004).
[3] Sandvik Phys. Rev. Lett. 98, 227202 (2007).

第18回

日時:10月13日15時より

場所:理学部1号館4階447号室

講演者:森貴司

講演タイトル:Generic long-time behavior of periodically driven quantum systems in high-frequency regime

講演要旨:
To understand the long-time behavior of periodically driven systems is one of the important and challenging problems in none quilibrium physics. In the high-frequency regime, the Floquet-Magnus expansion provides us a tool to describe a periodically driven system by using the static effective Hamiltonian. Recently, there are some attempts to realize interesting physical models as an effective Hamiltonian of a periodically driven system. In these studies, it is implicitly assumed that the syst em relaxes towards an equilibrium state of the effective Hamiltonian. However, theoretically, it is known that the Floquet-M agnus expansion is not a convergent series, and hence it is not obvious whether we can really use a finite-order truncation of the Floquet-Magnus expansion. Indeed, based on some numerical evidences, it has been argued that periodically driven syst ems finally reach the state of infinite temperature, which is different from the equilibrium state of the effective Hamilton ian. In this talk, I argue that a quantum system driven by a rapidly-oscillating field first relaxes to the equilibrium stat e of the effective Hamiltonian, and after a timescale exponentially long in frequency, the system will eventually relax to t he true stationary state.

第17回

日時:9月15日13時30分より

場所:理学部9号館9階934号室

講演者:Roy Chantrell(University of York)

講演タイトル:multi scale approaches to magnetic materials modelling

講演要旨:
N/A

第16回

日時:8月21日13時より

場所:理学部4号館3階1320号室

講演者:George Sudarshan(Center for Complex Quantum Systems, University of Texas at Austin, Austin, Texas, USA)

講演タイトル:Quantum Zeno Effect

講演要旨:
“When we continuously observe an unstable particle, its time evolution from the initial state is suppressed.” This inspiring proposal in 1976 by Baidyanath Mishra and George Sudarshan [1] has been well known as “Zeno’s paradox in quantum theory”, and has posed a great challenge in both theoretical and experimental fields. The proposal has required revision in the fundamental properties of quantum dynamics, measurement, and application to the control of quantum state, resulting in more than thousand papers until today.

Experimental evaluation of the proposal with unstable two- (or three-) levels system [2] revealed that the proposal is no more paradox, but a new vision of quantum physics called “quantum Zeno effect”. The extension of the concept produces hot discussion around “Anti quantum Zeno effect” [3] and “Zeno subspace” [4], to name the few [5].

In this special lecture, Prof. Sudarshan will provide a review on related studies, background philosophy of the proposal, and future opportunities/challenges of the concept to further deepen our understanding on the quantum dynamics.

References:
[1] B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18 (1977) 756.
[2] R. J. Cook, Phys. Scr. T 21 (1988) 49; W. M. Itano, D. J. Heizen, J. J. Bollinger and D. J. Wineland, Phys. Rev. A 41 (1990) 2295 ; S. R. Wilkinson, et.al. Nature 387 (1997) 575.
[3] A. M. Lane, Phys. Lett. A 99(1983) 359.
[4] P. Facchi, G. Marmo, S. Pascazio, A. Scardicchio, and E.C.G.Sudarshan, J. Opt. B: Quantum Semicl. Opt. 6 (2004) S492.
[5] A fine review on this topics can be found in: P. Facchi, G. Marmo andS. Pascazio, J. Phys. : Conf. Ser. 196 (2009) 012017.

第15回

日時:7月21日15時より

場所:理学部1号館4階447号室

講演者:Fabio Bagarello(DEIM, Universit di Palermo, Viale delle Scienze)

講演タイトル:a mathematical model of alliances in politics

講演要旨:
We discuss a dynamical model for a decision-making process in politics. In particular, we deduce the time evolution of what we call decision functions for three political parties interacting among them and with different groups of electors. These decision functions describe the will of the parties to form, or not, some political alliance. We show that an essential aspect in the possibility of getting some final decision is the interaction of the parties with the electors. In absence of such an interaction, no final decision is deduced.

第14回

日時:7月14日15時より

場所:理学部1号館4階447号室

講演者:安田勇輝(東京大学大学院理学系研究科 地球惑星科学専攻)

講演タイトル:An investigation on an atmospheric phenomenon "Stratospheric Sudden Warming" in terms of equilibrium statistical mechanics

講演要旨:
There exists the largest vortex called the polar vortex (perimeter: a half of the equator) in the stratosphere (height: 10-50 km) over the polar region in winter. The polar vortex sometimes breaks within a few days with an increase in temperature. This phenomenon is called Stratospheric Sudden Warming. We investigated the Stratospheric Sudden Warming using a theory of equilibrium statistical mechanics. This theory predicts the final structure of large-scale vortex field after strong mixing of vortices. We obtained a phase diagram with a region where metastable states exist, and compared it with numerical simulations and a meteorological reanalysis dataset. It is shown that the Stratospheric Sudden Warming can be qualitatively interpreted as the relaxation towards the equilibrium from the metastable state.

第13回

日時:7月7日15時より

場所:理学部1号館4階447号室

講演者:島田尚

講演タイトル:An “Ising model” of open and evolving systems

講演要旨:
An important and universal feature of real complex systems, such as social, economic, engineering, ecological, and biologica l systems, is that those are open: in those systems, constituting elements are not fixed and the complexity emerges (at leas t persist) under successive introductions of new elements. Those systems sometimes grow, but also sometimes collapse. Theref ore why and when, in general, we can see such open and complex systems is a fundamental question.

In this talk, I revisit this classical problem using our very simple “Ising model”. I will show that this model gives eith er continuous growth or stagnation in system size, depending on the model’s unique parameter: the average number of interac tions per element. And from a mean-field theory of it, we can find that this transition essentially originates from a balanc e of two effects: although having more interactions makes each element robust, it also increases the net impact of the loss of an element to the system [1]. This novel relation might be a origin of the moderately sparse (~10 of average degree) netw ork structure and the non-trivial distribution function of the lifetime of elements, both of those we often find in real sys tems. I will also argue the relation between an ordinary diffusion process (Ornstein-Uhlenbeck process) and our model, espec ially how that fails to explain the transition [2].

[1] T. Shimada “A universal transition in the robustness of evolving open systems”, Scientific Reports Vol. 4, 4082 (2014).
[2] T. Shimada, in Springer monograph “Mathematical Approaches to Biological Systems: networks, Oscillations and Collective Motions” (Springer, 2015).

第12回

日時:6月30日15時より

場所:理学部1号館4階447号室

講演者:Cristian Enachescu(Alexandru Ioan Cuza University)

講演タイトル:Cluster growth in various 2D and 3D shapes of spin crossover compounds in the framework of elastic models

講演要旨:
The spin transition compounds are molecular magnets, switchable between two states in thermodynamic competition: the diamagnetic low spin state (LS) and the paramagnetic high spin state (HS). They are composed of transition-metals ions having four to seven electrons in their valence d-shell situated in an octahedral ligand field, which splits the d orbitals into antibonding eg and weakly bonding t2g orbitals. Due to a higher occupancy of the eg orbitals in high-spin molecules, their molecular volume is larger than the one of low spin molecules. The difference in molecular volume between the two possible spin states induces distortions of the sample lattice during the transition, which are are at the origin of intermolecular interactions. When the elastic interactions in these systems are stronger than a threshold value, the abrupt transition is accompanied by complex hysteresis processes, non-random distributions of HS and LS molecules, nucleation and growth phenomena.

Based on the so-called ball and string concept and on the realistic idea that the difference of molecular volumes in the two states is at the origin of elastic interactions and induces a shift of the molecules in the system during the transition, elastic models have been recently elaborated for the study of spin crossover compounds.

Here we study the cluster growth either 2D lattices with different shapes (rectangular, hexagonal, circular or elliptic) or 3D face-centered cubic and hexagonal close-packed systems with open boundaries, composed of individual molecules arranged at the vertices of a triangular tiling and linked by springs. The switching of a molecule between the two states is decided using a Monte Carlo standard procedure with Arrhenius, Metropolis, Eden or Kawasaki dynamics, with transition probabilities depending on the temperature, the energy and enthalpy differences between states and the local pressure determined by the elongation or compression of its closest springs.

References
[1] C. Enachescu, M. Nishino, S. Miyashita, K. Boukheddaden, F. Varret, P. A. Rikvold, Phys. Rev. B, 91, 104102, 2015
[2] C. Enachescu, L. Stoleriu, A. Stancu, A. Hauser, Phys. Rev. Lett., 102, 257204, 2009
[3] C. Enachescu, M. Nishino, S. Miyashita, ”Theoretical descriptions of spin-transitions in bulk lattices”, in “Spin-crossover materials - properties and applications”, John Wiley & Sons, Chichester, UK, 2013

第11回

日時:6月23日15時より

場所:理学部1号館4階447号室

講演者:桂法称

講演タイトル:Exact ground states and topological order in interacting Kitaev chains

講演要旨:
We study a system of interacting spinless fermions in one dimension which, in the absence of interactions, reduces to the Kitaev chain [1]. A signal of topological order in the non-interacting case is the appearance of zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of repulsive interactions when the chemical potential is tuned to a particular function of the other parameters. Then we prove that the obtained ground states are adiabatically connected to the ground states of the free-fermion chain without gap closing. We also demonstrate explicitly that there exists a set of Majorana operators that can be thought of as an interacting generalization of edge zero modes in the original Kitaev chain.

[1] A. Yu. Kitaev, Phys.-Usp. 44, 131 (2001), cond-mat/0010440.

第10回

日時:6月16日15時より

場所:理学部1号館4階447号室

講演者:Gonzalo Ordonez(Department of Physics and Astronomy, Butler University)

講演タイトル:Impurity-Controlled Transport within a Finite Disordered Lattice

講演要旨:
We consider a finite disordered 1D quantum lattice with an attached impurity. We study the transport of a single electron fr om the impurity to the lattice at zero temperature. The transport is dominated by Anderson localization and in general it ha s a random character due to the lattice disorder. However we show theoretically that, by adjusting the impurity energy, the electron can attain quite regular, periodic motions. In particular, by a precise tuning of the impurity energy, the electron can be set to oscillate between the impurity and lattice sites far from the impurity, at distances larger than the Anderson localization length, and with long periods of oscillation. This phenomenon may be observable in analogous optical systems.

第9回

日時:6月9日15時より

場所:理学部1号館4階447号室

講演者:Per Arne Rikvold(Florida State University)

講演タイトル:Phase Diagrams for an Ising Model with Competing Short-range Antiferromagnetic and Long-range Ferromagnetic Interactions

講演要旨:
Many systems contain a mixture of short-range and long-range interactions, e.g., physical systems with both exchange and elastic or electrostatic interactions, or social systems with a combination of interactions within a close group and with the larger society. Well-studied examples of the former are spin-crossover materials, in which the long-range interaction is usually elastic [1]. Many of the properties of phase transitions in such mixed-interaction systems can be studied with simplified models, such as Ising models with nearest-neighbor and weak long-range (equivalent-neighbor or Husimi-Temperley) interactions. If both interactions are attractive (ferromagnetic), it is known that any nonzero long-range interaction strength changes the universality class of the phase transition to the classical mean-field class [1,2]. However, when the short-range interaction is antiferromagnetic and the long-range interaction is ferromagnetic, the line of antiferromagnetic phase transitions caused by the short-range interaction remains in the Ising universality class, now separated by critical endpoints or tricritical points from lines of discontinuous transitions at low temperatures [3]. A detailed study of the phase diagrams for the latter case with an elastic long-range interaction is computationally very demanding [3]. Here, I therefore discuss a simplified model, in which the long-range interaction is of the Husimi-Temperley type. Using mean-field theory andMonte Carlo simulations, I present detailed phase diagrams for various values of the long-range interaction constant. While simple, two-sublattice mean-field calculations show only a line of critical points, separated from lines of discontinuous phase transitions by tricritical points. However, the Monte Carlo simulations show richer phase diagrams, in some cases including critical endpoints and predicting interesting hysteresis patterns for real systems. Due to fluctuations caused by the competition between the two interaction types, this simplified model still presents significant numerical challenges that have required the development of novel techniques for flat-histogram evaluation of the density of states [4].

[1]. S. Miyashita, Y. Konishi, M. Nishino, H. Tokoro, and P. A. Rikvold, Phys. Rev. B *77*, 014105 (2008).
[2]. T. Nakada, P. A. Rikvold,T. Mori,M. Nishino,and S. Miyashita, Phys. Rev. B *84*, 054433 (2011).
[3]. M. Nishino and S. Miyashita, Phys. Rev. B *88*, 014108 (2013).
[4]. G. Brown, P. A. Rikvold, and S. Miyashita, Phys. Proc. *57*, 20-23 (2014).

第8回

日時:6月2日15時より

場所:理学部1号館4階447号室

講演者:藤堂眞治

講演タイトル:Tensor Network Algorithm for 2D Frustrated Magnets

講演要旨:
Frustrated quantum magnets exhibit various exotic quantum phases, such as gapful/gapless quantum spin-liquid phases, etc. The standard quantum Monte Carlo method, however, suffers from the notorious "negative sign problem" in simulating frustrated magnets at low temperatures. The tensor network algorithm is one of the most promising numerical methods for investigating such quantum states of many-body systems. In this seminar, after reviewing the basics of tensor network algorithm, we apply the method to the J1-J2 Heisenberg model on the square lattice. Especially, we focus on the stability of stripe Neel phase for large J2 region. The convergence of imaginary time evolution of tensor network state is also discussed.

第7回

日時:5月26日15時より

場所:工学部6号館2階64講義室

講演者:Ferenc Kun(University of Debrecen)

講演タイトル:Fracture and fragmentation of heterogeneous materials under compression

講演要旨:
Several aspects of the mechanical failure of heterogeneous materials are dominated by the disorder which is typically present at the micro and meso scales. Due to this reason the investigation of fracture and fragmentation processes provides also interesting challenges for statistical physics. Here we study the compressive failure of geo-materials as a laboratory analog of the emergence of earth quakes. We develop a realistic discrete element model of sedimentary rocks and simulate how the sample approaches catastrophic failure when subject to uniaxial compression. We show that crackling noise can be well represented by rupture cascades of the cohesive contacts of cemented particles. All statistical features of these breaking bursts have been found to have good agreement with laboratory experiments and field observations. To characterize the approach to failure we study the records of the time series of bursts and demonstrate that the record breaking sequence may give early warning of the imminent catastrophe. In spite of the slowly increasing load the sample gets fragmented along a damage band. Our simulations revealed that large fragments have a fractal shape with power law distributed mass. In spite of the slow loading the mass distribution exponent proved to be the same as for energetic fragmentation, which shows the robustness of the fragmentation universality class.

第6回

日時:5月19日15時より

場所:理学部1号館4階447号室

講演者:伊藤伸泰

講演タイトル:Factors of urban traffic

講演要旨:
Social applications are becoming one of major fields of HPC applications. Agent-based simulations and so-called the "big data" are the main tools of such social applications. Available "big data" are often not big enough to make out what is happening, and simulation results of agent-based models are necessary to get it. Application to urban traffic flow, which is reported in this talk, will be an example of such social applications. Real traffic data is limited, and simulation model which reproduces real traffic is used to make surrogate data. We did factor analyses of multivariate statistics for surrogate data of traffic flows, major factors of traffic jams are estimated.

第5回

日時:5月12日15時より

場所:理学部1号館4階447号室

講演者:桑原知剛

講演タイトル:Universal character of metastability in periodically driven systems

講演要旨:
We investigate the periodic dynamics of isolated quantum many-body systems. Generically, such systems are known to heat up to infinite temperature in the thermodynamic limit, while the behaviors for finite time scales is still a challenging issue. Even if a state goes to the chaotic state under infintite-time periodic dynamics, the state may remain a metastable state with rich structures. Indeed, the existence of such metastable states has been reported in periodically driven Friedrichs mo dels;that is, we still have the possibility to construct the universal Floquet theory at a finite time scale.

Here, we give several universal properties of finite-time Floquet theory. We mathematically prove the existence of the metas table states, whose lifetimes exponentially increases with the driving frequency ω. In the proof, they are given by the eigenstat es of a Hamiltonian which comes from the finite-order truncation of Floquet-Magnus expansion; there, we prove that the Floquet-Magnus expansion exponentially converges by a certain order of O(ω) and then breakdown beyond it. This way, the Floquet Hamiltonian can be well-approximated by the Floquet-magnus expansion for finite-time scale, although it might look completely random for the infinite-time limit. To relate our result to the physically interesting phenomenon, we prove exponentially slow heat absorption for the driving frequency, which is relevant to so called many-body energy localization.

References
[1] Takashi Mori, Phys. Rev. A 91, 020101(R) (2015).

第4回

日時:4月28日15時より

場所:理学部1号館4階447号室

講演者:羽田野直道

講演タイトル:Analytic calculation of non-adiabatic dynamicsaround an exceptional point

講演要旨:
We analytically compute the non-adiabatic dynamics around an exceptional point of a $2\times 2$ non-Hermitian matrix. By numerically integrating the Schr\"{o}dinger equation, Gilary, Mailybaev and Moiseyev [1] found a very interesting phenome non in the non-adiabatic dynamics. It is well-known that the two eigenstates that would coalesce at the exceptional point are swapped into each other if we enc ircle the exceptional point quasi-statically. Surprisingly, Gilary \textit{et al.}\ noticed that if we encircle it non-adiabatically starting from any states, the final s tate is one of the two eigenstates; if we encircle it in the other direction, the final state is the other one.

We here confirm this observation by using a model dynamics that allows us to compute the non-adiabatic time-evolution analyt ically; the final result is obtained as analytic functions. In the calculation, we utilized a useful triangularization devised by Hashimoto [2].

[1] I. Gilary, A. Mailybaev, N. Moiseyev. Time-asymmetric quantum-state-exchange mechanics, Phys. Rev. A, 88 (2013), 051102.
[2] K. Hashimoto, K. Kanki, H. Hayakawa, T. Petrosky, Non-divergent representation of non-Hermitian operator near the except ional point with application to a quantum Lorentz gas, Prog. Theor. Exp. Phys., 2015 (2015) 023A02.

第3回

日時:4月21日15時より

場所:理学部1号館3階338号室

講演者:福島孝治(東京大学大学院総合文化研究科)

講演タイトル:Random first-order transition of a spin-glass model in three dimensions

講演要旨:
Mean-field theory of spin glasses has provided a number of novel concepts for understanding of a phase transition in disorde red glassy systems. In particular, replica-symmetry breaking (RSB) plays an essential role in describing complex free-energy structure. It turns out that the pattern of RSB is clarified into two distinct classes, full RSB and one-step RSB. Despite extensive studies including large-scale numerical simulations, no conclusion has been reached about the issue whether the RS B concepts survive in short-ranged spin-glass models in finite dimensions. In recent years, some mean-field spin-glass model s with the one-step RSB have attracted much attention of many researchers. These models are regarded as a prototype of a phe nomenological picture of structural glass transition, called random first-order transition (RFOT), which is characterized by a thermodynamic transition with a discontinuous order parameter without latent heat. The advisability of the RSB picture in finite dimensional spin glass models comes to an issue again in the context of the structural glass transition. In this tal k, we present some results of large-scale Monte Carlo simulations based on extended ensemble method for a spin-glass model in three dimensions. Our findings are fully compatible with those expected from the RFOT picture based on the one-step RSB.

T.Takahashi and KH, Phys. Rev. E 91, 020102(R) (2015)

第2回

日時:4月14日15時より

場所:理学部1号館4階447号室

講演者:宮下精二

講演タイトル:Effects of elastic interactions on phase transitions of systems with various types of short range interactions

講演要旨:
We have studied cooperative phenomena of spin-crossover type of materials, which consist of bistable state (e.g., HS and LS) and are modeled by Ising variable. But, the difference of energies, degeneracies, and volumes of the states causes various ordering processes. The volume difference causes distortion of the lattice and the elastic interaction affects the nature of phase transitions [1]. We have studied the effect in the ferromagnetic system [2], and antiferromagnetic system [3]. In the seminar, we discuss the effect on the antiferromagnets in the triangular lattice [4]. This model is atypical frustrated system and it is known to have double Kosterlitz-Thouless phase transitions if we add next-nearest-neighbor ferromagnetic interaction. In the low temperature phase, the model has a ferrimagnetic order and nonzero uniform magnetization. Thus we expect that the elastic interaction has relevant effect on the phase transition [4]. We will discuss this property.

[1] M. Nishino, K. Boukheddaden, Y. Konishi and S. Miyashita, Phys. Rev. Lett. 98, 247203 (2007),S. Miyashita, Y. Konishi, M. Nishino, H. Tokoro and P.A. Rilvold, Phys. Rev. B 77, 0144105 (2008).
[2] T. Nakada, P. A. Rikvold, T. Mori, M. Nishino, and S. Miyashita, Phys. Rev. B 84 054433 (2011), T. Nakada, T. Mori, S. Miyashita, M. Nishino, S. Todo, W. Nicolazzai and P. A. Rikvold, Phys. Rev. B 85, 054408 (2012).
[3] Masamichi Nishino, and Seiji Miyashita, Phys. Rev. B 88, 014108 (2013).
[4] Masamichi Nishino, and Seiji Miyashita: in preparation.

第1回

日時:4月7日15時より

場所:理学部1号館4階447号室

講演者:新M1

講演タイトル:研究紹介

講演要旨:
N/A