UEDA GROUP
Department of Physics, The University of Tokyo

• 夏学期： 古典的論文のレヴューを行います。配布資料は英語、発表は英語もしくは日本語です。
• 冬学期： 研究結果の紹介もしくは研究に関係したレビューを行います。発表は英語です。
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 semeste (October 2021-January 2022)

木曜日13時からZoom上で行います(普段と場所or時間の異なる場合は赤字で示します)。
Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).
<Schedule>
Oct. 7 Joining of new B4 & M1 members
Oct. 14 Nakagawa
Oct. 21 Wang
Oct. 28 Matsumoto
Nov. 4 Sakamoto / Kawabata
Nov. 11 Mori
Nov. 18 Z. Liu
Nov. 25 K. Liu
Dec. 2 (No seminar)
Dec. 9 Sugimoto
Dec. 16 Dabelow
Dec. 23 Shiraishi
Jan. 6 Li
Jan. 13 Hara

2021/10/14 13:00-
 speaker Masaya Nakagawa title Exact eigenstates and weak ergodicity breaking in multicomponent Hubbard models abstract The $\eta$-pairing state is an exact superfluid eigenstate of the Fermi-Hubbard model constructed by C. N. Yang [1]. In this work, we construct exact eigenstates of multicomponent Hubbard models, which include the SU(N) Hubbard model as a special case, by generalizing the $\eta$-pairing mechanism [2]. The generalized $\eta$-pairing eigenstates are formed through simultaneous condensation of multiple types of fermion pairs and shown to exhibit off-diagonal long-range order coexisting with magnetic long-range order. Unlike the two-component case, these exact eigenstates do not arise from symmetry of the Hamiltonian, but originate from a restricted spectrum-generating algebra supported by the Pauli exclusion principle. Building on this fact, we show that the generalized $\eta$-pairing eigenstates do not obey the eigenstate thermalization hypothesis and can be regarded as quantum many-body scar states. This result indicates that the N-component Hubbard models show weak ergodicity breaking for $N \geq 3$. References: [1] C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989). [2] M. Nakagawa, H. Katsura, and M. Ueda, in preparation.

2021/10/21 13:00-
 speaker Zhikang Wang title Measurement induced phase fixation in discrete space abstract We find that in a lattice space, the wave function of free particles develop a fixed relation of its complex phases at different sites when general continuous position measurement is present, and as a consequence, the expectation value of the energy becomes constantly zero at each single trajectory level, and the expection value of the energy cannot be perturbed by the stochastic measurement outcome. We discuss the properties and the generality of this result, and we show how this phase relation is developed, and discuss the conditions for developing this phase relation.

2021/10/28 13:00-
 speaker Norifumi Matsumoto title Quantum many-body scar states in a Rydberg-atom chain with hopping abstract Recently, unusual initial states have been experimentally discovered which does not reach the thermal equilibrium for an anomalously long time in contrast to the rapid thermalization of the majority of initial states[1]. Motivated by this result, intensive research has been conducted investigating quantum many-body scar states, which exhibit an extremely slow thermalization or even absence of it. In the system discussed in Ref.[1], atoms trapped in an optical lattice are described as two-level systems, in which the high-energy level, called the Rydberg state, exhibits a strong repulsion with neighboring ones. Here, to gain an insight into the emergence of quantum many-body scar states and thermalization, we investigate the situation in which there are unoccupied sites and atoms can hop between nearest-neighbor sites, while in the original study atoms are fixed at each site. Specifically, we numerically obtain the energy spectrum and eigenstates as well as their entanglement entropy for a small number of sites and atoms. We show the existence of a series of low-entangled states and analyze their property. Furthermore, we discuss their influence on the dynamics and an algebraic relationship among some of them. (This research is conducted in the self-directed joint-research project as a part of the course work of the leading graduate school MERIT.) [1]H. Bernien et al., Nature 551, 579 (2017).

2021/11/4 13:00-
 speaker Yuki Sakamoto title Game-Theoretical Models on a Graph abstract Game theory is commonly used to explain human decision-making processes and has an important role in economics, biology and other various fields. In this seminar, we would see a game-theoretical model with a large population on a graph and Pairwise-Fermi update rule. We mainly focus on what is called the prisoner's dilemma game, where two rational players are likely to mutually defect and fail to reach the optimal choices for both players. In this model, a phase transition behavior can be observed with respect to the coefficient of cost-to-benefit ratio and the strength of natural selection.

 speaker Kohei Kawabata title Nonlinear Landauer Formula abstract The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear quantum Hall effect. We establish a new connection between the nonlinear quantum Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear quantum Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime. Reference: K. Kawabata and M. Ueda, arXiv:2110.08304

2021/11/11 13:00-
 speaker Takashi Mori title Heating in many-body systems under fast and strong driving abstract Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. Here, we provide a simple formula on the heating rate under fast and strong periodic driving in classical and quantum many-body systems. The key idea behind the formula is constructing a time-dependent dressed Hamiltonian by moving to a rotating frame, which is found by a truncation of the high-frequency expansion of the micromotion operator, and applying the linear-response theory to the dressed Hamiltonian, rather than the bare Hamiltonian. It is confirmed for specific classical and quantum models that the second-order truncation of the high-frequency expansion yields quantitatively accurate heating rates beyond the linear-response regime. Our result implies that the information on heating dynamics is encoded in the first few terms of the high-frequency expansion, although heating is often associated with an asymptotically divergent behavior of the high-frequency expansion. Reference: T. Mori, arXiv:2107.12587

2021/11/18 13:00-
 speaker Ziyin Liu title Stochastic Neural Networks with Infinite Width are Deterministic abstract In this work, we show the predictive variance of a trained stochastic neural network tends to zero as its width tends to infinity. Our results shed light on how stochastic neural networks work and have important implications for distribution modeling with neural networks and Bayesian deep learning.

2021/11/25 13:00-
 speaker Kangqiao Liu title An attempt to construct a quantum information engine on a tilted 1D periodic potential abstract Traditionally, people use Maxwell's demon to construct classical information engines by harnessing the thermal fluctuations. Recently, a minimal model of quantum information engine fueled by pure quantum measurements without the aid of a thermal bath has been proposed. It consists of a two-level system and work can be extracted by simply performing measurements on the qubit. We attempt to construct a quantum information engine in a tilted potential using measurement and feedback control. In this seminar, I'm going to review classical and quantum information engines, the Bloch oscillation, and then describe our problem setup.

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### 夏学期 / Summer semester (April-July 21)

<Regular seminars (review of seminal papers)>
木曜日13時からZoom上で行います(普段と場所or時間の異なる場合は赤字で示します)。
Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).

April 15 (Thu) Shoki Sugimoto
"The second laws of quantum thermodynamics"
F. Brandao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, Proc. Natl. Acad. Sci. U.S.A. 112, 3275 (2015)

April 22 (Thu) Norifumi Matsumoto
"Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder"
M. Znidaric, Phys. Rev. Lett. 110, 070602 (2013)

May 6 (Thu) Ziyin Liu
"Portfolio Selection"
H. Markowitz, The Journal of Finance 7, 1, 77-91 (1952)
"Empirical properties of asset returns: stylized facts and statistical issues"
R. Cont, Quantitative Finance, 1, 223-236 (2001)

May 13 (Thu) Zhikang Wang
"Bose-Einstein condensation in the alkali gases: Some fundamental concepts"
A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001)
"Theory of Bose-Einstein condensation in trapped gases"
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999)

May 20 (Thu) (No seminar)

May 27 (Thu) (No seminar)

June 3 (Thu) Kohei Kawabata
"Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model"
F. D. M. Haldane, Phys. Lett. A 93, 464 (1983)
"Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State"
F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)

June 10 (Thu) Yuki Sakamoto
"Non-Abelian anyons and topological quantum computation"
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, Rev. Mod. Phys. 80, 1083 (2008)
"Introduction to topological quantum computation with non-Abelian anyons"
Bernard Field and Tapio Simula, Quantum Sci. Technol. 3 045004 (2018)

June 17 (Thu) 12:30- Kangqiao Liu
"The fluctuation-dissipation theorem"
R. Kubo, Rep. Prog. Phys. 29 255 (1966)

June 24 (Thu) Hyuntae Moon
"Simple mathematical models with very complicated dynamics"
R. M. May, Nature 261, 459-467 (1976)

July 1 (Thu) Tatsuki Odake
"Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer"
P. W. Shor, SIAM J. Comput., 26(5), 1484-1509 (1997)
"Algorithms for quantum computation: discrete logarithms and factoring"
P. W. Shor, Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124-134 (1994)

July 8 (Thu) Koki Shiraishi
"A Gallavotti-Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics"
J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 365 (1999)

July 15 (Thu) (No seminar)