セミナー

1-form Lieb-Schultz-Mattis theorem and anomaly matching in quantum dimer model

2018年6月8日(金) 13:30 - 17:00

菊池 勇太 (理化学研究所 仁科加速器科学研究センター (RNC) 理研BNL研究センター 理論研究グループ 理研BNLセンター研究員)

The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and U(1) charge conservation are both preserved. In this talk, we discuss the generalization of the Lieb-Schultz-Mattis theorem to systems with higher-form symmetries, which act on extended objects of dimension n > 0. The prototypical lattice system with higher-form symmetry is the pure abelian lattice gauge theory whose action consists only of the field strength. We first construct the higher-form generalization of the Lieb-Schultz-Mattis theorem with a proof. We then apply it to the U(1) lattice gauge theory description of the quantum dimer model on bipartite lattices. Finally, using the continuum field theory description in the vicinity of the Rokhsar-Kivelson point of the quantum dimer model, we diagnose and compute the mixed ’t Hooft anomaly corresponding to the higher-form Lieb-Schultz-Mattis theorem.

会場: SUURI-COOL (Kyoto)

イベント公式言語: 日本語

Abelian-Higgs dualities in quantum defect-mediated melting phase transitions

2018年4月27日(金) 14:30 - 17:30

Aron Beekman (慶應義塾大学)

In the study of zero-temperature quantum phase transitions, instead of looking how symmetry is broken, it is often useful to see how symmetry can be restored by the condensation of topological defects. Through a duality mapping, Nambu-Goldstone modes are represented as gauge bosons, mediating long-range interactions between topological defects. When the latter condense, those bosons get as mass via the Anderson-Higgs mechanism, which signals the loss of rigidity and the restoration of symmetry. I will first review the best-studied case: the 2+1D superfluid-insulator transitions where the defects are U(1) vortices. Consecutively several extensions are discussed: going to 3+1D where the defects are not point particles but strings, and quantum elasticity, which studies breaking of spatial translations and rotations.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Thermodynamic of a one-dimensional Bose gas at low temperature & superfluidity in neutron-star matter

2018年4月24日(火) 15:30 - 16:30

Giulia De Rosi (The Institute of Photonic Sciences, Barcelona, Spain)

Ultracold atomic gases and neutron-star matter play a paramount importance in many-body physics, by exhibiting important analogies and differences. One of the most interesting phenomena shared by both systems is provided by superfluidity. In the first part of the talk, I will show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures T, I demonstrate that the coefficient in the $T^2$ expansion of the chemical potential is defined by the zero-temperature density dependence of the sound velocity and it has been calculated along the crossover between the Bogoliubov weakly-interacting gas and the Tonks-Girardeau gas of impenetrable bosons. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations. In the second part of the talk, I will show the results of a study of the superfluid gap in pure neutron matter, associated with the formation of Cooper pairs in the $^1S_0$ channel. The interaction responsible of the onset of superfluidity is an effective interaction coming from a nuclear Hamiltonian strongly constrained by phenomenology and obtained from the correlated basis function (CBF) perturbation theory and the formalism of cluster expansions. The calculations have been carried out using an improved version of the CBF effective interaction, in which three-nucleon forces are taken into account using a microscopic model. Our results show that the superfluid transition occurs at values of densities corresponding to the neutron-star inner crust.

会場: セミナー室 (160号室)

イベント公式言語: 英語

基本解近似解法による点渦力学系の数値解析

2018年4月17日(火) 16:00 - 17:30

榊原 航也 (京都大学 大学院理学研究科 特定助教)

iTHEMS / KUAMSジョイントセミナー

会場: 京都大学 北部総合教育研究棟 1階 益川ホール

イベント公式言語: 日本語

Including an ocean mixing model in atmospheric data assimilation: a case of Typhoon Soudelor 2015

2018年4月17日(火) 15:00 - 15:30

高玉 孝平 (理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム 特別研究員)

会場: 京都大学 北部総合教育研究棟 1階 益川ホール

イベント公式言語: 英語

Resurgence Theory for Non-Perturbative Quantum Analysis

2018年3月28日(水) 13:00 - 15:00

三角 樹弘 (数理創造プログラム 客員研究員 / 秋田大学 専任講師)

会場: セミナー室 (160号室)

イベント公式言語: 英語

Introduction to exact WKB analysis

2018年3月27日(火) 10:00 - 12:00

岩木 耕平 (名古屋大学)

会場: セミナー室 (160号室)

イベント公式言語: 英語

Anomaly matching for spin chains

2018年3月19日(月) 14:00 - 16:00

谷崎 佑弥 (理化学研究所 仁科加速器科学研究センター (RNC) 理論研究グループ 基礎科学特別研究員)

会場: セミナー室 (160号室)

イベント公式言語: 英語

Several identities related to the degenerate Bernoulli polynomials and numbers

2018年2月24日(土) 16:00 - 17:00

Takao Komatsu (Professor, Wuhan University, China)

In this talk we demonstrate some relations in degenerate Bernoulli polynomials, which may be expressed as a general convolution identity. We also show some properties of hypergeometric degenerate Bernoulli polynomials and numbers.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Diophantine Frobenius Problems — counting theory, generating function and zeta functions

2018年2月23日(金) 16:00 - 17:00

Takao Komatsu (Professor, Wuhan University, China)

When a_1, ...,a_m are relatively prime positive integers, the number of solutions of the linear Diophantine equation a_1 x_1 + … + a_m x_m = b in non-negative integers x_1, ...,x_m, for any integer b, is our concern. We show several formulas to give the largest integer b without solution. Then we discuss the generating function of the number of solutions. Finally, we derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies a set of new identities for the Hurwitz zeta function.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Statistical mechanics of tissue homeostasis

2018年1月22日(月) 14:00 - 15:00

川口 喬吾 (東京大学)

Adult tissues undergo rapid turnover as mature cells are continuously lost and new cells arise through cell division. The balance between the gain and loss of cells must be finely orchestrated to maintain tissues, but how this balance is achieved remains largely unknown. Previous works [1] have used universal scaling laws to claim that the fate choice of stem cells (division or differentiation) are made strictly cell-autonomously. However, we recently recorded every stem cell fate choice within the mouse skin epidermal regions over one week and found that, far from being cell-autonomous, stem cell loss by differentiation is compensated by direct neighboring division [2]. In this talk, I will describe a model of tissue homeostasis using a macroscopic nonequilibrium setup, and explain how the coarse-graining of this model will lead to the effective dynamics of the voter model (DP2). I will show how we can use the property of dynamical crossover in the model -from the cell-autonomous regime (critical birth-death model) to the fate-coordinated regime (voter model)- to measure the length and time scales of stem cell coordination. I will then explain the pitfall in two-dimensions of using scaling relations for the clonal fate trace of cells, and present the workaround we used in the data analysis to definitively show the existence of cell-to-cell fate correlation.

会場: コモンルーム (246-248号室)

イベント公式言語: 英語

高密度天体現象と状態方程式

2017年12月28日(木) 10:30 - 11:30

古澤 峻 (数理創造プログラム 基礎科学特別研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

体内時計の普遍性と種特異性に関する数理的研究

2017年12月27日(水) 16:00 - 17:00

黒澤 元 (数理創造プログラム 研究員 / 理化学研究所 望月理論生物学研究室 研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

網膜細胞モザイクパターン形成の数理モデリング

2017年12月27日(水) 13:30 - 14:30

小川 軌明 (理化学研究所 理論科学連携研究推進グループ (iTHES) 特別研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

作用素のトポロジーとトポロジカル絶縁体

2017年12月27日(水) 10:30 - 11:30

窪田 陽介 (数理創造プログラム 研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

Chiral Phases in Frustrated 2D Antiferromagnets and Fractional Chern Insulators

2017年12月21日(木) 11:00 - 12:00

Eduardo Fradkin (University of Illinois, USA)

会場: 研究本館 5階 535-537号室

イベント公式言語: 英語

Baryon Asymmetry of the Universe generated by Helical Hypermagnetic fields through chiral anomaly

2017年12月20日(水) 11:00 - 12:00

Kohei Kamada (Center for Theoretical Physics of the Universe, Institute for Basic Science, Republic of Korea)

Recent observations of TeV blazars by Fermi identified deficits of secondary GeV cascade photons.These observations can be explained by intergalactic magnetic fields, which may have a primordial origin.If the magnetic fields are helical and generated before the electroweak symmetry breaking,nontrivial interaction between (hyper)magnetic fields and other particles can cause some interestingand non negligible phenomena in the early Universe. In this talk, I will show that the baryon asymmetry can be generated by the chiral anomaly and this mechanism might be responsible for the present baryon asymmetry of the Universe. The intergalactic magnetic fields are its smoking-gun. If this mechanism is responsible for the present Universe,the BSM physics is needed for the generation of (hyper)magnetic fields but not for the baryogenesis.

会場: セミナー室 (160号室)

イベント公式言語: 英語

A New Look at Matrix Models for QCD3

2017年11月24日(金) 16:30 - 18:00

金澤 拓也

Non-chiral random matrix models for QCD in 2+1 dimensions and their new generalizations will be discussed.

会場: セミナー室 (160号室)

イベント公式言語: 英語

The Riemann-Roch theorem

2017年9月26日(火) 14:00 - 15:00

窪田 陽介 (数理創造プログラム 研究員)

In the mid- 19th century, B. Riemann introduced the notion of Riemann surface in his Ph.D thesis on complex analysis. Together with non-Euclidean geometry, the theory of Riemann surface is a germination of modern geometry in both algebraic and analytic sense. In this talk, I will give an introduction of the theory of Riemann surface centering around the Riemann-Roch theorem. It is an important prototype of the Atiyah-Singer index theorem, the starting point of my research field.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Connections of Pair Correlations to Equidistribution and Additive Energy

2017年8月31日(木) 13:30 - 15:00

Thomas Lachmann (Graz University of Technology, Austria)

会場: コモンルーム (246-248号室)

イベント公式言語: 英語