<Schedule>
Apr. 13 Li
"Zur Theorie der Metalle I. Eigenwerte und Eigenfunktionen der
linearen Atomkette."
Hans Bethe, Zeitschrift f¨ur Physik 71, (3-4): 205-226 (1931)
"Spin-Wave Spectrum of the Antiferromagnetic Linear Chain."
Jacques des Cloizeaux and J. J. Pearson, Phys. Rev. 128, 2131 (1962)
"Spectrum and scattering of excitations in the one-dimensional
isotropic Heisenberg model."
L. D. Faddeev and L. A. Takhtadzhyan, Journal of Soviet Mathematics 24, 241-267 (1984)
Apr. 20 K. Liu
"Generalized entropic uncertainty relations"
H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)
Apr. 27
May. 4 (National Holiday)
May. 11 Z. Liu
"Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex."
Amit, Daniel J., and Nicolas Brunel. Cerebral cortex 7.3 (1997): 237-252.
May. 18 Shiraishi
"Atomic Coherent States in Quantum Optics"
F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).
"Some properties of coherent spin states"
J. M. Radcliffe, J. Phys. A: Gen. Phys. 4, 313 (1971).
May. 25
Jun. 1 Sakamoto
"Multiparty entanglement in graph states"
M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A 69, 062311 (2004).
Jun. 8 Sugimoto
"On a general evolution criterion in macroscopic physics"
P. Glansdorff and I. Prigogine, Physica 30, 351 (1964).
"On Symmetry-Breaking Instabilities in Dissipative Systems"
I. Prigogine and G. Nicolis, J. Chem. Phys. 46, 3542 (1967).
"Symmetry Breaking Instabilities in Dissipative Systems. II"
I. Prigogine and R. Lefever, J. Chem. Phys. 48, 1695 (1968).
Jun. 15 Sugiura
"Many-Body Problems in Quantum Statistical Mechanics. I. General Formulation"
T.D Lee and C.N.Yang, Phys. Rev. 113, 1165 (1958).
Jun. 22 Takama (B4 student)
"Periodic table for topological insulators and superconductors"
A. Kitaev, AIP Conf. Proc. 1134, 22 (2009).
Jun. 29
Jul. 6 Ishii
"Quantum critical phenomena"
J. A. Hertz, Phys. Rev. B 14, 1165 (1976).
Jul. 11 (Tue) Hokkyo
"Measures on the Closed Subspaces of a Hilbert Space"
A. M. Gleason, J. Math. Mech. 6, 885 (1957).
"Quantum States and Generalized Observables: A Simple Proof of Gleason’s Theorem"
P. Busch, Phys. Rev. Lett. 91, 120403 (2003).
speaker | Shoki Sugimoto |
title | Eigenstate Thermalization for Translation Invariant Spin Systems |
abstract |
Reconciling the dynamics of microscopic theory with thermalization of many-body systems postulated in thermodynamics and statistical mechanics has been a fundamental problem since the era of Boltzmann.
Recent experimental result has enabled us to realize isolated quantum systems, and their thermalization has been observed.
On the other hand, the unitary time evolution of isolated quantum systems preserves the purity of the state.
Therefore, isolated quantum systems cannot relax to a mixed state, such as a thermal ensemble, if they are initially in a pure state.
The eigenstate thermalization hypothesis (ETH) is now believed to be the key to reconciling these seemingly conflicting facts.
It states that every eigenstates of a many-body Hamiltonian is indistinguishable from the microcanonical ensemble in terms of physically relevant operators, such as local or few-body ones.
The ETH ensures thermalization of the system from any initial state and has been verified to hold in various nonintegrable systems.
Under the presence of symmetry, the ETH usually holds within each symmetry sector.
However, several numerical studies report that local quantities satisfy the ETH without separating momentum sectors in the presence of translational symmetries.
In this talk, we prove an instance of these numerical observations. Namely, we show that local operators satisfy the ETH with the optimal speed of convergence in translation invariant spin systems [1]. We prove this fact as Theorem in the full random-matrix regime, where the Hamiltonian contains highly nonlocal and O(N)-body terms, and numerically show that it generically remains true for locally interacting systems. Our theorem applies to spin systems with arbitrary spin quantum numbers on rectangular lattices of arbitrary dimensions. [1] S. Sugimoto, J. Henheik, V. Riabov, and L. Erdős, J. Stat. Phys. 190, 128 (2023). |
speaker | Masaya Nakagawa |
title | Symmetry-protected topological feedback control |
abstract |
Symmetry and topology are guiding principles for the classification of quantum phases of matter. For instance, unique gapped ground states of quantum many-body systems are classified into symmetry-protected topological phases, where different phases cannot be continuously connected with each other while preserving symmetry and an energy gap [1]. One can also utilize symmetry and topology to classify nonequilibrium dynamics. Examples include Floquet topological phases with topological unitary operators [2] and non-Hermitian topological phases in open systems [3]. Here, we develop a framework of a topological classification of quantum channels that describe discrete quantum feedback control [4]. We show that only ten symmetry classes out of the 38-fold Bernard-LeClair classes are consistent with projective measurement. Building on the symmetry classification, we construct symmetry-protected topological feedback control, which exhibits helical spin transport due to nontrivial point-gap topology.
[1] X. Chen, Z. C. Gu, Z. X. Liu, and X. G. Wen, Phys. Rev. B 87, 155114 (2013). [2] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010). [3] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018). [4] M. Nakagawa and M. Ueda, in preparation. |
speaker | Shuma Sugiura |
title | Feedback Cooling of a Quantum Harmonic Oscillator |
abstract | Quantum feedback is more difficult than classical feedback due to the existence of a measurement backaction. I present a new method of feedback cooling which is analytically solvable and seemingly easy to implement. |
speaker | Takashi Mori |
title | Open-system analysis of thermalization in isolated quantum systems |
abstract |
Eigenstate thermalization hypothesis (ETH) explains why an isolated quantum system eventually thermalizes, but it does not tell us much about the timescale of the onset of thermalization. Since the time evolution is unitary, all the eigenvalues of the time evolution operator lie on the unit circle in complex plane. It means that we cannot estimate the thermalization timescale by looking at eigenvalues of the time evolution operator. In this talk, I explain that an open-system analysis based on the Lindblad quantum master equation is helpful to estimate the thermalization timescale of the isolated system [1]. It shows that isolated systems are better characterized as the weak dissipation limit of the dissipative dynamics. More specifically, we consider a kicked Ising chain under bulk dissipation and investigate the Liouvillian gap, which is the spectral gap of the generator of the dynamics, in the weak dissipation limit. We show that the Liouvillian gap can remain finite even in the weak dissipation limit if the thermodynamic limit is taken first. This finite value of the Liouvillian gap in the weak dissipation limit gives the exponential decay rate of the isolated system. This result is reminiscent of Ruelle-Pollicott resonances in classical chaos. Indeed, we argue that the finite Liouvillian gap in the weak dissipation limit is interpreted as a quantum Ruelle-Pollicott resonance. For static systems with the time-independent Hamiltonian, a special care is needed. I also explain how we can extract exponential decays hidden in the unitary time evolution of a static system. [1] T. Mori, in preparation. |
speaker | Yuki Sakamoto |
title | Pink-noise dynamics in an evolutionary game on a regular graph |
abstract | Modern game theory has been applied to various fields such as politics, psychology and biology. In particular, some game theoretical-models are considered to explain development of cooperative relation even in social viscosity in a large population. In recent years, several mechanisms have been found to construct sustainable cooperation by giving players mutual advantages and keeping them from undesirable risk avoidance. One mechanism is a network structure. We consider a multiplayer prisoner’s dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and obtain heatmaps of the fraction of cooperators. In the heatmap, there is a mixed region where cooperators and defectors coexist. Pink-noise behavior is observed in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. It is found that the pink-noise behavior can be reproduced in a simple random-walk model. |
speaker | Hongchao Li |
title | Law of Balance and Stationary Distribution of Stochastic Gradient Descent |
abstract |
The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this work, we prove that the minibatch noise of SGD regularizes the solution towards a balanced solution whenever the loss function contains a rescaling symmetry. Because the difference between a simple diffusion process and SGD dynamics is the most significant when symmetries are present, our theory implies that the loss function symmetries constitute an essential probe of how SGD works. We then apply this result to derive the stationary distribution of stochastic gradient flow for a diagonal linear network with arbitrary depth and width. The stationary distribution exhibits complicated nonlinear phenomena such as phase transitions, broken ergodicity, and fluctuation inversion. These phenomena are shown to exist uniquely in deep networks, implying a fundamental difference between deep and shallow models.
[1]: Z. Liu, H. Li, M. Ueda, arXiv: 2308.06671. |
speaker | Koki Shiraishi |
title | Entanglement and LOCC (local operation and classical communication) |
abstract |
This seminar will consist of the following three parts: ・ Introduction to the field of distributed quantum processing, ・ Decoding of stabilizer code by single-qubit local operations and classical communication, ・ Entanglement cost of quantum measurement. The first part is an introduction to how the distributed quantum information processing setting can be used to understand the nature of entanglement. By considering what kind of operations and tasks can be done by utilizing entanglement, we can understand the power of entanglement. Next, based on Ref. [1], we will explain how to extract quantum information distributed over multiple qubits by encode to stabilizer code, without using entanglement. Before understanding the power of entanglement, it is important to understand what tasks can be performed without entanglement. Finally, I will briefly discuss a study I am currently working on that quantitatively evaluates the entanglement required for a quantum measurement. The results will allow us to determine a lower bound on the amount of entanglement needed to accurately perform a given quantum measurement. [1] Koki Shiraishi, Hayata Yamasaki, and Mio Murao, "Efficient decoding of stabilizer code by single-qubit local operations and classical communication", arXiv:2308.14054. |
speaker | Akihiro Hokkyo |
title | Ergotropy and passivity in quantum many-body system |
abstract |
There are two independent characterizations of thermal equilibrium states in quantum theory: passivity and the consistency with statistical mechanics.
The former corresponds to Plank's principle in macroscopic thermodynamics, which is one formulation of the second law. This principle asserts that no positive work can be extracted in an adiabatic cycle.
The latter means that thermal equilibrium states should have the same expectation values with the ones of the microcanonical state with respect to thermal observables.
If all eigenstates satisfy the latter condition, it is called the eigenstate thermalization hypothesis(ETH) holds.
These properties have been well studied, but their relationship is not clear. In fact, ETH in quantum many-body systems and passivity are naively incompatible.
In this talk, I will discuss about maximal extractable work, ergotropy, in many-body system, and the relationship to themality via observables. I will show that ergotropy can be bounded by athermality of initial state and entanglement entropy decrease by operation. As a corollary, we find that ETH implies passivity of eigenstates in generalized sense. |
speaker | Takanao Ishii |
title | Finding nonequilibrium steady states of open quantum systems |
abstract |
One of the promising approaches to understanding nonequilibrium system is to focus on the nonequilibrium steady states (NESS). The first part of this seminar is about one of the numerical methods to calculate NESS of open quantum systems that can be described by GKSL equation. In 2019, 4 independent groups published papers on variational method using RBM ansatz simultaneously. This method is thought to be superior to conventional methods since it can be applied to 2 dimensional or even higher dimensional systems. The presenter will thoroughly review this method and present the verification result. The second part is the analytical result on a simple toymodel, which is spin 1/2 dissipative Heisenberg model. Although this model is very simple, it provides us important insights on Lindblad dynamics, which will be a foothold to more complex models. |
speaker | Shumpei Ishida |
title | Open system approach to light-induced anomaous Hall effect in graphene |
abstract |
Non-equilibrium phenomena have been discovered in optically driven quantum solids. In fact, anomalous Hall current was observed by illuminating graphene with circularly polarized light [1]. This current is not only originated from the Berry curvature, but also from the non-equilibrium electron population bias [2]. However, validity of the dissipation introduced in Ref. [2] is unclear because it is based on the phenomenological assumption. For example, the dissipation does not hold the locality. Here, we numerically observed the anomalous Hall effect by introducing dissipation from the microscopic model. We also simulated a nonlinear current with respect to voltage, which could not be considered with linear response theory. This is a proposal for a microscopic method of calculating Hall currents that does not use linear response theory and does not require phenomenological assumptions. Our quantum master equation approach is expected to have the potential to analyze non-equilibrium phenomena beyond the linear response regime and to analyze thermal Hall effects. [1] McIver, J.W., Schulte, B., Stein, FU. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020). [2] S. A. Sato, J. W. McIver, M. Nuske, et al. Microscopic theory for the light-induced anomalous Hall effect in graphene. Phys. Rev. B 99, 214302 |
speaker | Prof. Eric Lutz (University of Stuttgart) |
title | Thermodynamics of non-Markovian feedback control |
abstract |
Feedback control mechanisms play an essential role in regulating physical, biological and engineering systems. The standard second law of thermodynamics does not hold in the presence of measurement and feedback. Most studies so far have have extended the second law for discrete, Markovian feedback protocols. However, non-Markovian feedback is omnipresent in processes where the control signal is applied with a non-negligible delay. I will discuss generalized second laws for non-Markovian feedback, including fluctuation theorems and the effect of acausality. I will further present experimental results based on an optically levitated microparticle [1,2]. [1] Thermodynamics of continuous non-Markovian feedback control, Nature Communications 11, 1360 (2020). [2] Non-Markovian feedback control and acausality: an experimental study, Physical Review Letters 128, 200601(2022). |