Department of Physics, The University of Tokyo
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2022年 / Academic Year 2022

研究室メンバーによるレギュラー・セミナー、 および、他研究室・機関からのゲスト・スピーカーのセミナーを開催しています。 レギュラー・セミナーは下記要領で行います。 Access map:理学部1号館 (Faculty of Science Bldg. 1) / 理学部4号館 (Faculty of Science Bldg. 4)

冬学期 / Winter semester (October 2022-January 2023)

    Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).
Oct. 6 Joining of new B4 & M1 members
Oct. 13 Matsumoto
Oct. 20 (No seminar)
Oct. 27 (No seminar)
Nov. 3 (National Holiday)
Nov. 10 Shiraishi/Wang
Nov. 17 Nakagawa
Nov. 24 Z. Liu
Dec. 1 Sugimoto/Dabelow
Dec. 8 Sakamoto
Dec. 15 Li/Mori
Dec. 22 Sugiura/K. Liu

2022/10/13 13:00-
speaker Norifumi Matsumoto
title Renormalization group as a dynamical system in the classical Yang-Lee critical phenomenon
abstract The Yang-Lee edge singularity is a quintessential non-unitary critical phenomenon, which exhibits some anomalous scaling laws unseen in unitary critical phenomena. A prototypical example that exhibits this critical phenomenon is the classical one-dimensional ferromagnetic Ising model with a purely-imaginary external magnetic field. It has been pointed out that the real-space block renormalization group (RG) in this model can be represented as the logistic map of a certain parameter and that this RG involves chaotic flows.
In this seminar, we discuss the physical meaning of the chaotic behavior of the RG flows focusing on the change of the length scale in a correlation function under the RG transformation. Furthermore, we regard the RG transformation as a dynamical system, and we consider the relationship between the stability of a periodic orbit of this dynamical system and the analyticity of the free-energy density. In particular, we argue that the value of the coefficient in the logistic map appearing as the RG transformation has a physically reasonable consequence, that is, the parameter point corresponding to the Yang-Lee edge is the only periodic point of the logistic map at which the free-energy density exhibits a criticality. Finally, we argue that unstable periodic orbits except for the Yang-Lee edge exhibit non-analyticity originating from a discrete scale invariance rather than a criticality.

2022/11/10 13:00-
speaker Koki Shiraishi
title Locality of Quantum Master Equation in Quantum Many-Body Systems
abstract The Lindblad equation is a common approach to investigate the open quantum many-body systems. One microscopic approach to derive the Lindblad equation is the rotating-wave approximation, however, it is not justified in many-body systems and non-equilibrium systems. Therefore, various derivations are suggested in the literature of the open quantum many-body system.
In this seminar, first I review these derivations of the Lindblad equation and how do they differ. Then, I will introduce our approach to derive the Lindblad equation by localizing Redfeild equation based on the Lieb-Robinson bound. I also show numerical results and explain when such derivations are valid in many-body systems.

speaker Zhikang Wang
title Convergent Deep Reinforcement Learning for Quantum Control of Continuous-Space Systems
abstract Despite recent success of deep reinforcement learning in various fields, current deep reinforcement learning techniques typically suffers from instability and can lead to lack of consistency and lack of reproducibility of results. To solve the problem so that the reinforcement learning technique can be better applied to physical problems, we develop a convergent deep Q network algorithm as a modification to the conventional deep Q network (DQN) algorithm, and we show that our algorithm is indeed convergent and that it removes a few instability problems of DQN in numerical experiments. Next, we consider applying the algorithm to the measurement-feedback cooling problem of a quantum mechanical rigid body, and we discuss the specifications and the properties of the system.

2022/11/17 13:00-
speaker Masaya Nakagawa
title Topology of discrete quantum feedback control
abstract Feedback control, which is an operation conditioned on a measurement outcome on a system of interest, provides a versatile tool in a wide range of disciplines from science to engineering. It also plays an important role in the fundamental laws of physics, a famous example being Maxwell's demon in thermodynamics. In this seminar, we propose a topological characterization of discrete quantum feedback control. By exploiting a mapping from quantum channels to non-Hermitian operators, a topological invariant of a CPTP map is defined. We construct a model of quantum Maxwell's demon with nontrivial non-Hermitian topology and demonstrate a non-Hermitian skin effect induced by feedback control.

2022/11/24 13:00-
speaker Ziyin Liu
title Collapse and Phase Transitions in Deep Learning
abstract It was recently discovered that deep learning features a series of very common phenomena that are called "collapses," where the learned representation becomes low-rank. In this presentation, I discuss how different types of collapses can be potentially unified under a phase transition framework.

2022/12/01 13:00-
speaker Shoki Sugimoto
title Eigenstate Thermalization and Constraints On Observables
abstract The eigenstate thermalization hypothesis (ETH), which states that every energy eigenstate of a generic quantum many-body system is indistinguishable from the thermal ensemble, is considered to be the primary mechanism behind the thermalization of generic isolated quantum systems. It has been recognized that some constraints on observable quantities, such as locality or few-bodiness, are necessary for the ETH. Still, the quantitive effect of these constraints on the ETH has remained unclear. In this seminar, we reveal how the ETH depends on constraints on observables by introducing a new measure of distinguishability between two quantum states that explicitly reflects our ability on the measurements. For fully chaotic many-body quantum spin systems in any spatial dimension, whose eigenstates are distributed over the Haar measure, we analytically find that the ETH typically holds even if we observe all of the m-body operators with m = O(N) as least when m/N is smaller than a threshold. We also identified how many-body operators we need to measure to distinguish between eigenstates and ensembles.

speaker Lenert Dabelow
title Automated computer algebra via reinforcement learning
abstract Computer algebra systems (CAS) have become an indispensable tool in modern theoretical sciences. Key features of such software packages include simplifying mathematical terms, finding derivatives, or solving equations in symbolic form. These capabilities are typically based on a huge database of rules for how a specific operation (e.g., differentiation) transforms a certain term (e.g., sine function) into another term (e.g., cosine function). Thus far, these rules needed to be discovered and subsequently programmed by humans. Focusing on the paradigmatic example of solving algebraic equations, we demonstrate how the process of finding elementary transformation rules and step-by-step solutions can be automated using reinforcement learning with deep neural networks.

2022/12/08 13:00-
speaker Sakamoto Yuki
title Iterated Prisoner's Dilemma Game on a Graph and Dynamics
abstract Game-theortetical models are applied in various fields to describe the learning dynamics in a large population. We discuss an iterated priosner's dilemma game on a regular graph. From the numerical result, we see a pink-noise behavior, whose spectral density is proportional to a power function of frequency.

2022/12/15 13:00-
speaker Hongchao Li
title Yang-Lee Singularity in BCS Superconductivity
abstract We investigate the Yang-Lee singularity in BCS superconductivity, and find that the zeros of the partition function accumulate on the boundary of a quantum phase transition, which is accompanied by nonunitary quantum critical phenomena. By applying the renormalization-group analysis, we show that Yang-Lee zeros distribute on a semicircle in the complex plane of interaction strength for general marginally interacting systems.

speaker Takashi Mori
title Projective resetting in deep neural networks
abstract In modern machine learning, we use a huge neural network such that the number of parameters greatly exceeds the number of training data samples, which is called the overparameterized regime. It is a fundamental problem to understand why overparameterized deep neural networks can achieve great generalization performance without serious overfitting. There are some approaches in theoretical studies, but here I focus on the role of the optimization algorithm, i.e. the stochastic gradient descent (SGD). Some recent studies reported that SGD happens in a tiny subspace: parameters change within a subspace whose dimension is much smaller than the total number of parameters. Indeed, in the simple linear regression problem, it is shown that the SGD dynamics is strictly restricted to the subspace spanned by Hessian eigenvectors with nonzero eigenvalues. Those observations indicate that not all the degrees of freedom are actually used in training, which leads to a great reduction of the degrees of freedom of a neural network. Motivated by the theoretical analysis on the linear regression problem, we propose the reduction of the degrees of freedom by projecting the parameters onto the M top Hessian subspace, which is spanned by Hessian eigenvectors with M top eigenvalues. We find that SGD dynamics projected onto the subspace yields comparable or even better generalization performance compared with the original dynamics. Moreover, we propose a new method of projective resetting, in which we project a trained network onto the top Hessian subspace and train it again. It turns out that the projective resetting significantly improves the generalization performance. This result indicates that “unnecessary” parameters in the orthogonal subspace have not only detrimental effects leading to overfitting, but also beneficial effects on generalization.

2022/12/22 13:00-
speaker Shuma Sugiura
title TBA
abstract TBA

speaker Kangqiao Liu
title Maxwell's Demon for Quantum Transport
abstract Maxwell's demon can be utilized to construct quantum information engines similarly to the classical Szilard engine. While most of the existing quantum information engines harness thermal fluctuations, quantum information engines that harness quantum fluctuations have recently been proposed. We here propose a new type of genuinely quantum information engine that can store useful work cumulatively by harnessing quantum fluctuations and achieve unidirectional transport of a particle on a tilted 1D lattice. There is no ambiguity in evaluating the power and velocity of our proposed engine in contrast to other existing quantum information engines that can also transport a particle. We find a tradeoff relation obeyed by the achievable maximum power and maximum velocity. We also propose an improved definition of efficiency by clarifying all possible energy flows involved in the engine cycle.