統計力学セミナー予定表 2014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)


日時 場所 講演者(敬称略) 講演題目


日時 講演者(敬称略) 講演題目
1月13日15時 坂下達哉(藤堂研究室、CMSI神戸拠点) Exact diagonalization package using integrated interface for parallel eigensolvers
12月16日15時 Mariagiovanna Gianfreda(Department of Physics, Washington University、羽田野研究室) Theoretical formulation and experimental realization of PT-symmetric systems
11月25日15時 添田彬仁(東大理村尾研究室) Quantum contextuality and itsquantification via correlation function
11月18日15時 Kimmo Kaski(BECS, Aalto University School of Science, Finland & CABDyN Complexity Center, Said Business School, Oxford University, UK) Social Physics Approach to Human Sociality: Computational Analysis and Modeling
11月11日15時 羽田野直道 Much fun with non-Hermitian quantum mechanics
11月4日15時 桑原知剛 Many-body entanglement and reversibility for external disturbance
10月7日15時 伊藤伸泰 Simulation of network traffic and applications
7月15日15時 島田尚 Will an open complex system be robust?
7月8日15時 吉岡直樹(伊藤研究室) Kinetic Monte Carlo algorithm for thermally induced breakdown of fiber bundles
7月1日15時 諏訪秀麿 Singlet-basis Projection Monte Carlo and Gap Analysis of Quantum Spin Systems
6月24日15時 森貴司 Natural correlation between a system and a thermal reservoir
6月17日15時 鈴木秀幸(東京大学大学院情報理工学系研究科) Chaotic Boltzmann Machines: Billiard Dynamics for Monte Carlo Simulation
6月10日15時 Cristian Enachescu(Alexandru Ioan Cuza University) New challenges in elastic models for spin crossover compounds
6月3日15時 藤堂眞治 Phase Transition and Universality of Quantum Spin Systems with Strong Spatial Anisotropy
5月27日15時 高安秀樹(ソニーCSL,明治大先端数理) コロイド粒子のアナロジーで見る金融市場の変動
4月22日 宮下精二 Landau-Zener process and Stoner-Wohlfarth process
4月15日 新M1 研究紹介
4月8日 Javier Campo(CSIC-University of Zaragoza) Neutron Scattering Studies of Molecule Based Magnets
過去のセミナー: 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





講演タイトル:Exact diagonalization package using integrated interface for parallel eigensolvers

As exact diagonalization package for quantum lattice model, TITPACK2 is widely used. However, TITPACK2 is not MPI parallelized.It makes eigenvalue computation for a large number of sites difficult. To overcome this situation, we need to employ opensource hybrid parallelized eigensolvers. Due to complicated structure of these solvers, there are few users of them. So, we started to develop integrated interfaces Rokko for dense solvers (EigenExa, ScaLAPACK etc.) and sparse ones (Anasazi, SLEPc). Based on Rokko, we develop diagonalization package for quantum XYZ model. We will report on progress of the developments.




講演者:Mariagiovanna Gianfreda(Department of Physics, Washington University)

講演タイトル:Theoretical formulation and experimental realization of PT-symmetric systems

It has been recently discovered that the requirement for a Hamiltonian to be Hermitian can be weakened to include complexnon-Hermitian PT-symmetric Hamiltonians; that is, Hamiltonians that are symmetric under combined space reflection P and timereversal T. This much wider class of Hamiltonians are physically acceptable because they possess two crucial features: (i) their eigenvalues are all real, and (ii) they describe unitary time evolution [1].
In this talk I will briefly describe the mathematical background on which PT-symmetric quantum mechanics is based; in particular I will introduce the C operator [2], i.e., the operator that equips a PT-symmetric quantum theory with a positive defined scalar product. I will then explain how PT-symmetric physical systems can be experimentally realized. In fact, in the last few years, a big amount of experiments based on PT-symmetric systems are being performed [3], among which, optical PT-symmetric systems can exhibit interesting features such as unidirectional invisibility and perfect transmission. Finally, I will mention a number of long-standing theoretical problems that have been solved by means of the techniques of PT symmetry, focusing the attention on one of them: the famous old problem of runaway modes in classical electromagnetism [4], that can be re-examined from the point of view of PT invariance to eliminate the classical runaway modes and to obtain a corresponding quantum system that is ghost free[5].

[1] C. M. Bender, Rept. Prog. Phys.70, 947-1018 (2007); A. Mostafazadeh, J. Geom. Methods Mod. Phys.7, 1191 (2010).
[2] C. M. Bernder and M. Gianfreda, J. Phys. A: Math. Theor.46, 275306 (2013).
[3] A. Guo, et al., Phys. Rev. Lett.103, 093902, (2009); C.E. Ruter, et al., Nature Phys.6, 192 (2010); J. Schindler, et al., Phys. Rev. A84, 040101 (2011); L. Feng, et al., Science333, 729 (2011); A. Regensburger, et al., Nature488, 167, (2012); L. Feng, et al., Nature Mat.12, 108 (2012); S. Bittner, et al., Phys. Rev. Lett.108, 024101 (2012); N.M. Chtchelkatchev, et al., Phys. Rev. Lett.109, 150405 (2012); C. Zheng, et al., Phil. Trans. R. Soc. A371, 20120053, (2013); B. Peng, S. K. Ozdemir, F. Lei, F. Moni , G. L. Long, S. Fan, F. Nori, M. Gianfreda, C. M. Bender, L. Yang, Nature Physcis10 394, (2014).
[4] J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), chap. 17.
[5] C. M. Bender and M. Gianfreda, arXiv:1409.3828 [hep-th].





講演タイトル:Quantum contextuality and itsquantification via correlation function

It is a well-known fact that quantum theory forbids assignment of predetermined values to all observables even when a system is in a pure state. This property has been referred to as “quantum contextuality” (or, contextuality, for short) in the literature. The violation of Bell’s inequality can be regarded as a special instance of contextuality, while the idea of contextuality applies to more general setting than that of Bell’s. It was recently discovered that even the more general notion of contextuality can be quantitatively verified by a particular type of correlation function. In this talk, we review some of the key historical developments in the field and discuss recent advances in the quantification of contextuality via correlation function.




講演者:Kimmo Kaski(BECS, Aalto University School of Science, Finland & CABDyN Complexity Center, Said Business School, Oxford University, UK)

講演タイトル:Social Physics Approach to Human Sociality: Computational Analysis and Modeling

In today’s society social interactions takes place increasingly through Information Communication Technology (ICT), the events of which leave behind digital traces of individual behaviour as ever-growing datasets. The study of such data using computational analysis and modeling with Network Theory approach can give us unprecedented insight into human sociality. This was well-demonstrated by our analysis of the dataset of mobile phone communication-logs, confirming the Granovetterian picture for the social network structure, i.e. being modular showing communities with strong internal ties and weaker external ties linking them[1]. More recently the same dataset has allowed us to look at the nature of social interaction in more detail and from a different Dunbarian egocentric perspective, due to it including demographic data in the form of gender and age information of individual service subscribers[2]. With this we have got a deeper insight into the gender and age-related social behavior patterns and dynamics of close human relationships. Our analysis results demonstrate sex differences in the gender-bias of preferred relationships that reflect the way the reproductive investment strategies of both sexes change across the lifespan, in particular women's shifting patterns of investment in reproduction and parental care. These empirical findings inspired us to take the next step in network theory, namely developing models to catch some salient features of social networks and processes of human sociality in them. One of our first models, based on network sociology mechanisms for making friends, turned out to produce many empirically observed Granovetterian features of social networks, like meso-scale community and macro-scale topology formation[3]. In another model we have investigated the social implications of deception for opinion formation in coevolving social network, where we find that white or pro-social lies glue society together while black or anti-social lies create diversity[4]. To summarize we believe that the network theory approach to social systems combined with computational data analysis and modeling opens up a new perspective for studying and even predicting collective social phenomena.

[1]JP Onnela, J Saram ki, J Hyv nen, G Szab , D Lazer, K Kaski, J Kert sz, AL Barab si, PNAS 2007, 104, 7332-7336.
[2]V. Palchykov, K. Kaski, J. Kertesz, AL Barabasi, RIM Dunbar, SCIENTIFIC REPORTS, 2012, 2 , 370.
[3]JM Kumpula, JP Onnela, J. Saram ki, K. Kaski, J. Kertesz, Phys. Rev. Lett. 2007, 99, 228701.
[4]G. I iguez, T. Govezensky, R.I.M Dunbar, K. Kaski and R. A. Barrio et al., Proc. R. Soc. B 2014 281, 20141195.





講演タイトル:Much fun with non-Hermitian quantum mechanics

I have worked on non-Hermitian quantum systems since 1995. There are a couple of typical elementary questions that I often receive. First, many wonder what kind of physical meaning one can associate with complex eigenvalues. Second, some also suspect that non-Hermitian Hamiltonians are not diagonalizable. Third, some claim that there must be some inconsistency because the norm is not conserved. I will answer these questions by reviewing researches in the past.





講演タイトル:Many-body entanglement and reversibility for external disturbance

The low temperature physics of quantum spin system is governed by entanglement patterns and much effort has been devoted to analyze them.The entanglement is often featured as a restriction to the transformation between two states, which motivates u s to analyze many-body ground states in terms of a reversibility property.In this talk, we devise a new formulation of the reversibility;our approach can discriminate between states enjoying microscopic and macroscopic quantum phenomena. Based on it, we prove a strong necessary condition for the ground states of general k-local Hamiltonians including long-rang e interactions.By applying our theorem to the quantum critical points, we can derive a new fundamental inequality for the critical exponents based on the trade-off relationship between the spectral gap and the fluctuation.





講演タイトル:Simulation of network traffic and applications

Agent-based modeling and simulations of social phenomena are expected to be one of major applications of supercomputers. Social system consists of three components: traffic, economics and social relation., and study on traffic system started earliest among them. Starting from single-lane traffic flow, two-lane, branching and merging, and network traffic have been developed. In this talk, some traffic modeling and simulations are shown, and future application will be discussed.





講演タイトル:Will an open complex system be robust?

The stability/fragility of complex systems has attracted broad interest since after the pioneering theoretical works in 1970s (1).This talk reports a novel class of transition in the robustness of complex and OPEN systems (2). Openness is a key and universal feature of various complex systems such as ecosystems, reaction networks in living organisms, economical systems, and social communities: their complexity emerges as a result of successive introductions of new elements. Using our simple “Ising model” for such open systems, it is found that system either evolve toward infinitely large size or stay finite depending on the unique system parameter: the average number of interactions per element. Interestingly, this transition originates from the balance of the two effects. Although having more interactions makes each element robust, it also increases the impact of the loss of an element. This novel mechanism provides an another scenario for the classical problem of “complexity-stability/robustness” relation.

1) Gardner, M. R. & Ashby, W. R. “Connectance of large dynamic (cybernetic) systems: critical values for stability.” Nature 228, 784-784 (1970) and May, R. M. “Will a large complex system be stable?” Nature 238, 413-414 (1972).
2) TS “A universal transition in the robustness of evolving open systems” Scientific Reports 4, 4082 (2014). (http://www.nature.com/srep/2014/140213/srep04082/full/srep04082.html)





講演タイトル:Kinetic Monte Carlo algorithm for thermally induced breakdown of fiber bundles

Fiber bundle models are one of the most fundamental modelling approaches for the investigation of the fracture of heterogeneous materials being able to capture a broad spectrum of damage mechanisms, loading conditions, and types of load sharing. In the framework of the fiber bundle model we introduce a kinetic Monte Carlo algorithm to investigate the thermally induced creep rupture of materials occurring under a constant external load. We demonstrate that the method overcomes several limitations of previous techniques and provides an efficient numerical framework at any load and temperature values. We show for both equal and localized load sharing that the computational time does not depend on the temperature, it is solely determined by the external load and the system size. In the limit of low load where the lifetime of the system diverges, the computational time saturates to a constant value. Using this method we also check the Arrhenius law of lifetime for equal load sharing in the presence of any types of quenched disorder distributions. For localized load sharing we show the modified form of the Arrhenius law does hold even in the presence of quenched disorder.





講演タイトル:Singlet-basis Projection Monte Carlo and Gap Analysis of Quantum Spin Systems

The projection Monte Carlo method has been a powerful numerical approach for the ground-state calculation of many kinds of strongly-correlated quantum systems. In the simulation, the sampled state space can be restricted to the same "sector" of quantum numbers with the ground state. We will show an efficient projection Monte Carlo utilizing not only total S^z but also total S and wave number for quantum spin systems. The trial wave function is composed by the correlated singlet pairs and sampled as the boundary condition of the worldlines. This projection scheme is effective also for the spectral analysis. The excited states can be easily specified in each sector, and more rapid convergence can be achieved than corresponding finite-temperature simulation. Nevertheless, the spectral analysis from Monte Carlo data is generally ill-posed in a similar situation to the inverse Laplace transformation. To address this non-trivial inverse problem, we have invented an improved gap estimator that converges to the true value. Then it becomes possible to precisely calculate the energy gap from our estimator. We calculated the velocity of the bilayer Heisenberg model at the critical coupling from the gaps at several wave numbers. Moreover, we will show the Monte Carlo level spectroscopy for the two-dimensional J-Q model. The controversial transition point as a candidate of "the deconfined criticality" was extrapolated from the excitation-gap crossing point with surprisingly small finite-size correction.

[1] H. Suwa "Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems" Springer Theses 2014
[2] H. Suwa and S. Todo "Generalized Moment Method for Gap Estimation and Quantum Monte Carlo Level Spectroscopy" arXiv:1402.0847





講演タイトル: Natural correlation between a system and a thermal reservoir

Non-Markovian corrections to the Markovian quantum master equation of an open quantum system are investigated up to the second order of the interaction between the system of interest and a thermal reservoir. The concept of “natural correlation” is discussed. When the system is naturally correlated with a thermal reservoir, the time evolution of the reduced density matrix looks Markovian even in a short-time regime. If the total system was initially in an “unnatural” state, the natural correlation is established during the time evolution, and after that the time evolution becomes Markovian in a long-time regime. It is also shown that for a certain set of reduced density matrices, the naturally correlated state does not exist. If the initial reduced density matrix has no naturally correlated state, the time evolution is inevitably non-Markovian in a short-time regime.
As an application besides the system + bath model, the classical Brownian motion and its deviation from the overdamped limit will be briefly discussed.





講演タイトル: Chaotic Boltzmann Machines: Billiard Dynamics for Monte Carlo Simulation

In the field of machine learning, Ising spin models are recognized by the name of "Boltzmann machines", and applied to various learning problems. Recently, we proposed a deterministic implementation of Boltzmann machines, which is named chaotic Boltzmann machines [1,2]. Chaotic Boltzmann machines have chaotic billiard dynamics that yields samples from Ising spin models without any use of random numbers, and thus can be regarded as a type of deterministic Monte Carlo algorithm for Ising spin models. Although there is no theoretical explanation yet, our numerical results suggest that it works as a deterministic alternative to random Monte Carlo methods. We expect that chaotic Boltzmann machines are amenable to efficient hardware implementation, because they can be regarded as a coupled oscillator system composed of simple oscillators. This approach presents a novel mechanism for analog/chaos computing.

[1] H. Suzuki, J. Imura, Y. Horio, K. Aihara: Chaotic Boltzmann machines, Scientific Reports 3 (2013), 1610. http://www.nature.com/srep/2013/130405/srep01610/full/srep01610.html
[2] H. Suzuki: Monte Carlo simulation of classical spin models with chaotic billiards, Physical Review E 88 (2013), 052144. http://pre.aps.org/abstract/PRE/v88/i5/e052144




講演者:Cristian Enachescu(Alexandru Ioan Cuza University)

講演タイトル:New challenges in elastic models for spin crossover compounds

Spin transition molecules 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. 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, a new family of models have been recently elaborated for the study of spin crossover compounds. Such a ball and spring model, using the molecular dynamics approach, has been used for studying various processes such as the thermal and pressure hysteresis or relaxation phenomena in continuous and open boundary systems. The mechano-elastic model considering molecules linked by connecting springs, always in mechanical equilibrium condition, was first introduced for the study of HS-LS relaxation processes and it was subsequently adapted for the study of photophysical processes including the phenomenon of a light induced hysteresis and for the study of the evolution of clusters during the thermal transition. Though different by their approach and method, both the molecular dynamics and the mechano-elastic model led to similar conclusions and, particularly, using open boundary conditions are able to reproduce the cluster formation starting from edges or corners, in accordance with experimental data. In this talk, I will approach some new areas opened by the elastic models: shape of the clusters in non-rectangular systems, appearence of cracks during transition and the possibility to obtain, in special situations, a quantum efficiency higher than unity for the photoexcitation process - LIESST effect which determines the molecular switching. References

[1] C. Enachescu, L. Stoleriu, A. Stancu, A. Hauser, Phys. Rev. Lett., 102, 257204, 2009, Eur. J. Inorg. Chem, 2013 and ref. therein
[2] C. Enachescu, M. Nishino, S. Miyashita, et al, EPL, 91(2), 27003, 2010, Phys. Rev. B, 86(10), 054114, 2012
[3] M. Nishino, S. Miyashita, K. Boukheddaden et al. Phys. Rev. Lett, 98, 247203, 2007; Phys. Rev. B, 79, 012409, 2009, Phys. Rev. B, 98, 094303, 2013, and ref. therein





講演タイトル:Phase Transition and Universality of Quantum Spin Systems with Strong Spatial Anisotropy

Quantum phase transition and universality of two-dimensional Heisenberg antiferromagnets with spatial anisotropy are discussed. We present a method that optimizes the aspect ratio of a lattice during the Monte Carlo simulations and realizes the virtually isotropic lattice automatically. Based on the correlation lengths, the system linear lengths, including the imaginary-time direction for the quantum models, are tuned by the Robbins-Monro algorithm. The method enables us to compare directly the value of critical amplitude between different anisotropic models, and helps with identifying the universality class. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent non-universal behavior is attributed mainly to the strong size correction of the effective aspect ratio due to the existence of the cubic interaction.

Reference: S. Yasuda and S. Todo, Phys. Rev. E 88, 061301(R) (2013); JPS Conf. Proc. 1, 012127 (2014).






外国為替市場の詳細な板情報を分析することによって、市場における価格変動の メカニズムが、多数の分子の中を漂うコロイド粒子の運動のメカニズムと酷似し ていることを示す。100万ドル単位の売買注文一本がコロイド粒子の周りのひ とつの分子に対応しており、分子の動きを観測することで市場のコロイド粒子の 運動を記述するランジュバン方程式を導出し、市場の粘性係数を推定する。この 市場の分子集団のクヌッセン数を見積もると、連続体記述が破綻するぎりぎりの 程度の値であることがわかる。物質では直接観測することがほとんど不可能であ る分子ひとつひとつの動きが精密に観測できるという点において、この板情報は 統計物理学の貴重な研究対象であり、同時にそれは1日に400兆円ものお金が 流れる世界経済の根幹部分の研究でもある。

参考文献:Yura, Takayasu, Sornette, Takayasu, PRL,112, 098703 (2014).





講演タイトル:Landau-Zener process and Stoner-Wohlfarth process

Magnetization dynamics under sweeping field cross an avoided-level structure has been studied by the Landau-Zener mechanism. The process of magnetization process does not depend on the total spin $S$ as long as the spin is isotropic because the equation of motion of magnetization is the same as the Torque equation. In the process the spin motion is regarded as a motion of a vector with fixed length. However, in the case $S>1/2$ the system can have an anisotropy, and then the dynamics of magnetization cannot be adiabatic with the motion of field, which corresponds the jump in the Stoner-Wohlfarth process in the classical magnets. In the process of quantum case, the equation of motion causes a kind of entanglement, and the system exhibits a state which has no-classical correspondence. We will study the processes by making use of structure of eigenenergies.










講演者:Javier Campo

講演タイトル:Neutron Scattering Studies of Molecule Based Magnets

Neutron scattering techniques can provide fundamental insight into the different magnetic behaviors shown by molecule based magnets. In a short introduction the properties of the neutron-matter interactions (strong and magnetic dipolar) and the fundamentals of neutron scattering will be presented in order to facilitate an understanding of the peculiarities of this probe in molecule based magnets. Selected examples will be presented of the use of different neutron scattering techniques on very different molecular magnetic materials. S-based organic magnets. The sulphur based free-radical family p-X-C6F4CNSSN · (X = Br, NO2, CN) represents an alternative to the classical nitrogen-oxygen construct for the design of purely organic magnets. This example shows how to explore and understand the magnetic interaction mechanisms, via spin density determination using polarized neutron diffraction [1] Single molecule magnets. Single crystal neutron diffraction at very low temperatures and high magnetic field shows how the Mn12-acetate SMM can order via the magnetic dipolar interaction. However, for magnetic fields larger than 5 T it undergoes a quantum phase transition into a zero magnetization phase [2]. The effect of crystal disorder on quantum tunneling in the single-molecule magnet Mn12-benzoate will also be illustrated through measurements of the energy levels using inelastic neutron scattering [3]. Chiral magnets. The control of magnetic chirality in a material could be employed in spintronic devices in order to create or manipulate a spin-current. This example will show how neutron Laue diffraction can help to determine magnetic structures (and therefore the magnetic chirality) in very small crystals of [Cr(CN)6][Mn(S)-pnH(H2O)](H2O) [4]. Spin-crossover magnets. It has proved possible to determine the correlation between the motion of the pyrazine rings and the high-low spin transition in the spin crossover compound {Fe(pz)[Pt(CN)4]} by measuring quasi-elastic neutron scattering [5]. Spin-waves in Heisenberg Antiferromagnets. It is shown how it is possible to determine the magnetic interaction constants in molecular magnets by measuring the spin-wave dispersion curves with neutron triple axis spectroscopy [6].

[1] J. Luzón, et al. Phys Rev B. 81(2010).
[2] F Luis, J Campo et al. Phys Rev Let 95, 227202 (2005).
[3] Ch. Carbonera et al. Phys Rev B 81, 014427 (2010).
[4] J Campo et al. submitted.
[5] J. A. Rodríguez-Velamazán et al. JACS.
[6] J. Campo et al, Phys Rev B. 78, 054415 (2008).