セミナー
758 イベント
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セミナー
Mathematics of thermalization in isolated quantum systems
2020年11月10日(火) 16:00 - 18:10
白石 直人 (学習院大学 理学部 物理学科 助教)
If an isolated macroscopic quantum system is left at a nonequilibrium state, then this system will relax to the unique equilibrium state, which is called thermalization. Most of quantum many-body systems thermalize, while some many-body systems including integrable systems do not thermalize. What determines the presence/absence of thermalization and how to understand thermalization from microscopic quantum mechanics are profound long-standing problems. In the first part of my talk, I briefly review some established results of quantum thermalization. I first clarify the problem of thermalization in a mathematical manner, and then introduce several important results and insights: typicality of equilibrium states [1], relaxation caused by large effective dimension [2], and eigenstate thermalization hypothesis (ETH) [3,4] and weak-ETH [5]. In the second part of my talk, I explain some of my results. First, I introduce a model which is non-integrable and thermalizes but does not satisfy the ETH [6,7]. This finding disproves the conjectures that all nonintegrable systems satisfy the ETH and that the ETH is a necessary condition for thermalization. I also discuss the hardness of the problem of thermalization from the viewpoint of computational science [8]. Then, I move to an analytical approach to a concrete model, and prove that S=1/2 XYZ chain with a magnetic field is nonintegrable [9]. This is the first example of proof of nonintegrability in a concrete quantum many-body system, which will help a mathematical approach to thermalization.
会場: via Zoom
イベント公式言語: 英語
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Mathematical aspects of quasi-Monte Carlo integration
2020年11月5日(木) 16:00 - 18:10
鈴木 航介 (広島大学 大学院先進理工系科学研究科 助教)
In this talk, I will introduce mathematical aspects of quasi-Monte Carlo (QMC) integration. We aim to approximate the integral of a function on the d-dimensional hypercube [0,1]^d. A useful approach is Monte-Carlo (MC) integration, which uses randomly chosen samples. A drawback of MC is the rate of convergence; the standard deviation of the estimator converges as 1/sqrt(n) asymptotically in n. To have a better rate of convergence as O(log^d N/N) or more, QMC uses deterministic, uniformly distributed points. In the first part, I will give an overview of QMC, such as star-discrepancy, Koksma-Hlawka inequality, and some explicit constructions as lattices and digital nets. In the second part, I will show that QMC using lattices and digital nets can achieve a higher rate of convergence for smooth integrands.
会場: via Zoom
イベント公式言語: 英語
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Evolution of a peak of genetic divergence driven by local adaptation
2020年11月5日(木) 10:00 - 11:00
坂本 貴洋 (総合研究大学院大学 先導科学研究科 特別研究員)
In species that are distributed in various environments, each subpopulation adapts to the local environment. In general, when there is migration between subpopulations, genetic divergence does not proceed because the genomes are exchanged between subpopulations. However, around the loci involved in local adaptation, genetic divergence proceeds. This is because different genotypes are favored between subpopulations, so that the alleles of migrants are purged by natural selection and the exchange of genomes is suppressed. It has not been theoretically known how the degree of genetic differentiation evolves over time, making the interpretation of population genomic data difficult. In this study, we constructed and analyzed a model of population genetics to clarify the dynamics of genetic divergence.
会場: via Zoom
イベント公式言語: 英語
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Basics of population genomic data analysis
2020年10月29日(木) 10:00 - 11:00
ジェフリ・フォーセット (理化学研究所 数理創造プログラム (iTHEMS) 上級研究員)
In recent years, it has become possible to obtain the DNA sequence data of a large number of individuals of the same species. This data set is basically a M (number of samples) x N (number of genomic positions) matrix where each data point is 0 or 1. Using this data set, we try to understand, for example, the relationship between each sample or group of samples, and the population process that has generated the data set. In this talk, I will introduce the basic concepts behind the approaches we use to analyze such data sets.
会場: via Zoom
イベント公式言語: 英語
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Toward simulating Superstring/M-theory on a Quantum Computer
2020年10月23日(金) 17:00 - 18:00
花田 政範 (Department of Mathematics, University of Surrey, UK)
We present a framework for simulating superstring/M-theory on a quantum computer, based on holographic duality. Because holographicduality maps superstring/M-theory to quantum field theories (QFTs), we can study superstring/M-theory if we can put such QFTs on a quantum computer --- but it still looks like a complicated problem, if we use a usual lattice regularization. Here we propose an alternative approach, which turns out to be rather simple: we map the QFT problems to matrix models, especially the supersymmetric matrix models such as the Berenstein-Maldacena-Nastase (BMN) matrix model. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. It is straightforward to put the matrix models on a quantum computer, because they are just quantum mechanics of matrices, and the construction of QFTs is mapped to the preparation of certain states. We show the procedures are conceptually rather simple and efficient quantum algorithms can be applied. In addition, as a (kind of) byproduct, we provide a new formulation of pure Yang-Mills on quantum computer. If you would like to participate, please register using the form below.
会場: via Zoom
イベント公式言語: 英語
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Realistic shell model and chiral three-body force
2020年10月22日(木) 13:30 - 15:00
福井 徳朗 (京都大学 基礎物理学研究所 研究員)
We show an evolution to derive the effective Hamiltonian in the shell-model framework starting from two- and three-body interactions based on the chiral effective field theory. A new way to calculate three-body matrix elements of the chiral interaction with the nonlocal regulator is proposed. We apply our framework to the p-shell nuclei and perform benchmark calculations to compare our results with those by an ab initio no-core shell-model. We report that our results are satisfactory and the contribution of the three-body force is essential to explain experimental low-lying spectra of the p-shell nuclei. We discuss the contribution of the three-body force on the effective single-particle energy extracted from the monopole interaction. Next, we investigate the shell evolution on the pf-shell nuclei. We show that the monopole component of the shell-model effective Hamiltonian induced by the three-body force plays an essential role to account for the experimental shell evolution. Moreover, we present our latest results on the investigation of the possible neutron dripline of the Ca isotopes. Finally, we discuss very neutron-rich systems, namely, the oxygen isotopes at the dripline and beyond, where the interplay between the three-body force and continuum states plays an important role. If you would like to participate, please register using the form below.
会場: via Zoom
イベント公式言語: 英語
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Bayesian nonparametric estimation of Random Dynamical Systems
2020年10月21日(水) 14:00 - 15:00
Christos Merkatas (Postdoctoral Researcher, Aalto University, Finland)
In this talk, a Bayesian nonparametric framework for the estimation and prediction, from observed time series data, of discretized random dynamical systems is presented [1]. The size of the observed time series can be small and the additive noise may not be Gaussian distributed. We show that as the dynamical noise departs from normality, simple Markov Chain Monte Carlo method (MCMC) models are inefficient. The proposed models assume an unknown error process in the form of a countable mixture of zero mean normals, where a–priori the number of the countable normal components and their variances is unknown. Our method infers the number of unknown components and their variances, i.e., infers the density of the error process directly from the observed data. An extension for the joint estimation and prediction of multiple discrete time random dynamical systems based on multiple time-series observations contaminated by additive dynamical noise is presented [2]. In this case the model assumes an unknown joint error process with a pairwise dependence in the sense that to each pair of unknown dynamical error processes, we assign a– priori an independent Geometric Stick-Breaking process mixture of normals with zero mean. These mixtures a–posteriori will capture common characteristics, if there are any, among the pairs of noise processes. We show numerically that when the unknown error processes share common characteristics, it is possible under suitable prior specification to induce a borrowing of strength relationship among the dynamical error pairs. Then time-series with an inadequate sample size for an independent Bayesian reconstruction can benefit in terms of model estimation accuracy. Finally, possible directions for future research will be discussed.
会場: via Zoom
イベント公式言語: 英語
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セミナー
Composite Dark matter and gravitational waves
2020年10月20日(火) 10:00 - 11:00
リナルディ エンリコ (理化学研究所 数理創造プログラム (iTHEMS) 客員研究員 / AI Researcher/Engineer, Arithmer Inc.)
With non-perturbative lattice calculations we investigate the finite-temperature confinement transition of a composite dark matter model. We focus on the regime in which this early-universe transition is first order and would generate a stochastic background of gravitational waves. Future searches for stochastic gravitational waves will provide a new way to discover or constrain composite dark matter, in addition to direct-detection and collider experiments. As a first step to enabling this phenomenology, we determine how heavy the dark fermions need to be in order to produce a first-order stealth dark matter confinement transition.
会場: via Zoom
イベント公式言語: 英語
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A PDE model for the localization and spread of flu in the human respiratory tract
2020年10月14日(水) 10:00 - 11:00
クリスチアン・キルエットゥ (Ph.D. Student, Department of Medical Physics, Ryerson University, Canada)
Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But it also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus contents are also pushed along, upwards towards the nose and mouth. Our PDE model represents the HRT as a one-dimensional track extending from the nose down to the lower HRT, wherein stationary cells interact with virus which moves within (diffusion) and along with (advection) the PCF. In the PDE model, diffusion is negligible in the presence of advection which effectively sweeps away virus, preventing infection from spreading below the depth of deposition. Higher virus production rates (10-fold) are required at higher advection speeds (40 micron/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT located downstream of the advection flow see more virus than lower parts, and so infection grows, peaks, and resolves later in the lower HRT. Clinically, the infection would appear to progress from the upper towards the lower HRT, as reported in mice. When the PDE model is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. This new PDE model offers a convenient and unique platform from which to study the localization and spread of respiratory viruses (flu, RSV, COVID-19) within the HRT during an infection.
会場: via Zoom
イベント公式言語: 英語
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TQFT, integrable lattice model, and quiver gauge theories
2020年10月2日(金) 16:00 - 18:00
太田 敏博 (理化学研究所 数理創造プログラム (iTHEMS) 研修生 / 大阪大学 大学院理学研究科 博士課程)
1st part (math): In physics literature, “lattice models” appear quite often as mathematical models of physical systems, e.g. Ising model, vertex models, lattice gauge theory. The aim of the 1st part is to introduce ‘what is (T)QFT,’ ‘what is lattice model,’ and ‘what does integrability mean’ in the language of mathematics. In turn, they will play a crucial role in the 2nd part of my talk. I also hope that this will lead to a good exchange among us, especially between physicists and mathematicians. 2nd part (physics): In the 2nd part, I would like to explain where an integrable lattice model may come from, especially for people in the physics background. I will show a certain class of integrable lattice models is realized by Wilson-’t Hooft lines in 4d quiver gauge theories. I will also explain a bit how these gauge theories are constructed from brane configurations in string theory. String dualities allow us to relate the original 4d setups to 4d partially topological Chern-Simons theory, which is a partial TQFT and generates integrable lattice models. Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
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セミナー
The Uchuu Simulations: Data Release 1 and Dark Matter Halo Concentrations
2020年10月1日(木) 14:00 - 15:00
石山 智明 (千葉大学統合情報センター 准教授)
We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion dark matter particles in a box of 2.0 Gpc/h. The highest resolution simulation, called Shin-Uchuu, consists of 262 billion particles in a box of 140 Mpc/h. Combining these simulations we can follow the evolution of dark matter haloes (and subhaloes) spanning from dwarf galaxies to massive galaxy cluster hosts. We present basic statistics, dark matter power spectra and halo (subhalo) mass function, to demonstrate the huge dynamic range and superb statistics of the Uchuu simulations. From the analysis of the evolution of the power spectra we conclude that our simulations are accurate enough from the Baryon Acoustic Oscillations up to very small scales. We also provide parameters of a mass-concentration model, which describes the evolution of halo concentrations, that reproduces our simulation data within 5% error for haloes with masses spanning nearly eight orders of magnitude at redshift 0
会場: via Zoom
イベント公式言語: 英語
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Math Seminars by Dr. Genki Ouchi and Dr. Kenta Sato
2020年9月24日(木) 16:00 - 18:10
大内 元気 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)
佐藤 謙太 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)[Talk 1] (16:00 - 17:00) Dr. Genki Ouchi Automorphism groups of cubic fourfolds and K3 categories In this talk, I would like to talk about symmetries of algebraic varieties, especially cubic fourfolds and K3 surfaces. It is known that symmetries of cubic fourfolds and K3 surfaces are related to sporadic finite groups as Mathieu groups and Conway groups in both algebraic geometry and string theory. Relations between cubic fourfolds and K3 surfaces are studied in the context of derived categories, Hodge theory and so on. I would like to explain the direct relation among symmetries of cubic fourfolds and K3 surfaces via their derived categories. [Talk 2] (17:10 - 18:10) Dr. Kenta Sato An algebraic approach to the four color theorem The four color theorem states that, given any separation of a plane into contiguous regions, no more than four colors are required to color the regions. Although this theorem was already proved about 40 years ago, another proof without using a computer is not found still now. In this talk, I will introduce an algebraic approach to this theorem, which states that a conjecture about singularities of algebraic varieties implies the four color theorem. In particular, I would like to focus on the connection of three different fields in mathematics: graph theory, convex geometry and algebraic geometry. *Detailed information about the seminar refer to the email.
会場: via Zoom
イベント公式言語: 英語
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Phase Transitions in Biological Systems
2020年9月23日(水) 10:00 - 11:00
足立 景亮 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員 / 理化学研究所 生命機能科学研究センター (BDR) 生体非平衡物理学理研白眉研究チーム 基礎科学特別研究員)
Biological systems are built hierarchically by DNA, proteins, cells, tissues, organs, individuals, etc. Recent experiments have clarified the existence of interesting mesoscale phenomena inside cells, where the concept of condensed matter physics such as phase transition can be useful in its understanding. For example, interacting nucleosomes in a chromatin chain can cause the mega-base scale structural change, and sub-micron scale dense droplets of proteins/mRNAs can appear through phase separation. In this talk, I will discuss our recent topics: (i) structural transition of a chromatin with epigenetic marks, (ii) intracellular wetting of phase-separated droplets, and (iii) spontaneous aggregation of self-propelled individuals.
会場: via Zoom
イベント公式言語: 英語
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Eco-evolutionary dynamics with novel mutations
2020年9月16日(水) 10:00 - 11:00
Hye Jin Park (Junior Research Group Leader, Statistical physics of ecology and evolution group, Asia Pacific Center for Theoretical Physics, Republic of Korea)
Evolution is driven by individual birth and death that are determined by interactions between individuals. Hence studying interactions is crucial to understand the population evolution. However, traditional approaches dealt with those interaction structures are given while spontaneous random mutations can generate new interactors. We considered “mutant interactors,” which lead to new interactions between the residents and invading mutants that can drive the population away from the previous equilibrium and lead to changes in the population composition. Thus, first, we investigated the changes in the population size induced by mutant interactors[1]. And then, we applied this approach to answer the question about relationships between species[2]: Why is cyclic dominance so rare?
会場: via Zoom
イベント公式言語: 英語
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セミナー
Singular point implies coexistence in adaptive dynamics
2020年9月9日(水) 10:00 - 11:00
立川 正志 (理化学研究所 数理創造プログラム (iTHEMS) 客員研究員 / 京都大学 ウイルス･再⽣医学研究所 ⽣命システム研究部⾨ 准教授)
Adaptive dynamics is a relatively new mathematical framework for studying evolution(~1990s). Under the influence of the mathematical ecology and the game theory, adaptive dynamics considers the effect of resident populations on the fitness landscape. As a result, it explains a possible mechanism of evolutionary branching. In this talk, I introduce adaptive dynamics and Pairwise Invasibility Plot (PIP) analysis, a standard method for understanding the adaptive dynamics. Then, I propose a new approach to analyze the adaptive dynamics which enable us to understand higher dimensional systems than PIP does.
会場: via Zoom
イベント公式言語: 英語
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Maximal Regularity and Partial Differential Equations
2020年9月8日(火) 16:00 - 18:10
古川 賢 (理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 特別研究員)
The theory of maximal regularity is a powerful tool to get solutions having the best regularity to linear partial differential equations (PDEs) of parabolic type. The theory is also applicable to show well-posedness of various non-linear PDEs. In the first part, We introduce the history of the development of the theory of maximal regularity and the way to apply non-linear PDEs. In the second part, We give some applications to PDEs, e. g. the primitive equations, the Navier-Stokes equations, and elliptic equations with dynamic boundary conditions. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
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セミナー
Potential Toolkit to Attack Nonperturbative Aspects of QFT －Resurgence and related topics－
2020年9月7日(月) - 25日(金)
Aleksey Cherman (University of Minnesota, USA)
Gerald Dunne (University of Connecticut, USA)
Mithat Unsal (North Carolina State University, USA)
藤森 俊明 (慶應義塾大学)
初田 泰之 (立教大学)
本多 正純 (京都大学 基礎物理学研究所 助教)
森川 億人 (九州大学 博士課程)
居石 直久 (名古屋大学)
山崎 雅人 (東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU))Recently, there have been significant developments in theoretical techniques/frameworks to tackle non-perturbative aspects of quantum field theory (QFT) such as the resurgence theory, the Lefschetz thimble method, ’t Hooft anomaly matching, and novel lattice setups. Such developments are still growing very rapidly and making fruitful connections not only among physicists involved in fields with broad energy scales but also with mathematicians. These developments would enable us to unveil rich and exciting physics of QFT in the non-perturbative regime. It is of primary importance to hold a workshop for researchers in various fields related to the topics to get together and overview/share the recent progresses, to discuss future directions, and to seek for possible new collaborations bridging various fields of physics/mathematics. For more information, please see on the related link.
会場: YITP (Kyoto University), Zoom, and Mozilla hubs
イベント公式言語: 英語
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The hitch-hiker’s guide to the concept of adaptive dynamics
2020年9月2日(水) 10:00 - 10:30
入谷 亮介 (理化学研究所 数理創造プログラム (iTHEMS) 研究員)
Adaptation is of multi-causality, composed of mutation and selection processes. I will talk about how we model adaptation on the basis of the adaptive dynamics framework. This is a very quick, conceptual talk, rather than heavily mathematical, to draw attention from more people.
会場: via Zoom
イベント公式言語: 英語
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セミナー
Geometric Perspective for the Theory of Hydrodynamic Limits
2020年8月31日(月) - 9月1日(火)
佐々田 槙子
坂内 健一 (慶應義塾大学 理工学部 数理科学科 教授)This is a series of lectures on "Geometric Perspectives for Fluid Dynamic Limit Theory" by the following speakers: [DAY 1: Aug 31] Dr. Makiko Sasada (University of Tokyo) [DAY 2: Sept 1] Prof. Kenichi Bannai (Keio University) Abstract: One of the fundamental problems in the natural and social sciences is to explain macroscopic phenomena that we can observe from the rules governing the microscopic system giving rise to the phenomena. Hydrodynamic limit provides a rigorous mathematical method to derive the deterministic partial differential equations describing the time evolution of macroscopic parameters, from the stochastic dynamics of a microscopic large scale interacting system. In the article "Topological Structures of Large Scale Interacting Systems via Uniform Locality" joint with Yukio Kametani, we introduce a general framework encompassing a wide variety of interacting systems in order to systematically investigate various microscopic stochastic large scale interacting systems in a unified fashion. In particular, we introduced a new cohomology theory called the uniformly local cohomology to investigate the underlying geometry of the interacting system. Our theory gives a new interpretation of the macroscopic parameters, the role played by the group action on the microscopic system, and the origin of the diffusion matrix associated to the macroscopic deterministic partial differential equation obtained via the space-time scaling limit of the microscopic system. The purpose of the series of lectures is to introduce to the audience the theory of hydrodynamic limits, especially the relation between the macroscopic observables and the microscopic interacting system. We then explain our new perspective of how geometry comes into play in investigating the interacting system, and introduce the ideas and results of our article. *Detailed information about the seminar refer to the email.
会場: via Zoom
イベント公式言語: 英語
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セミナー
Modeling biological timing
2020年8月26日(水) 10:00 - 11:00
黒澤 元 (理化学研究所 数理創造プログラム (iTHEMS) 専任研究員)
Under stay-at-home situation, some of you may suffer from sleep disorder. Efficacy of a drug often depends on the timing of its prescription. We know this fact about our "timing", but we don't know why. This time, I wish to introduce two big mysteries in regard to biological timing. First is our internal daily clock. In general, biochemical process is believed to accelerate with temperature. In contrast, the period of our daily clock, made up of biochemical reactions is somehow stable to temperature. The prediction from simpler biochemical mathematical model, and its experimental verification will be presented. Second is hibernation. During winter, some birds and mammals decrease drastically their body temperature possibly to decrease their energy expenditure. Many studies about hibernation have been conducted for many years. However, basic mechanisms of hibernation (e.g. how the duration of hibernation is determined?) are largely unknown. Recently, we started to investigate body temperature time-series of hibernating hamsters over 100 days in the collaboration with experimental biologists. Preliminary results will be presented.
会場: via Zoom
イベント公式言語: 英語
758 イベント