論文 - 森　貴司

Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems

Shirai T., Mori T.

Physical Review Letters 133 （ 4 ）  2024年07月

ISSN  00319007

　概要を見る

Markovian open many-body quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the stationary state, but it has recently been pointed out that the spectral gap does not necessarily determine the overall relaxation time. Our understanding on the relaxation process before the asymptotically long-time regime is still limited. We here present a collective relaxation dynamics of autocorrelation functions in the stationary state. As a key quantity in the analysis, we introduce the instantaneous decay rate, which characterizes the transient relaxation and converges to the conventional asymptotic decay rate in the long-time limit. Our theory predicts that a bulk-dissipated system generically shows an accelerated decay before the asymptotic regime due to the scrambling of quantum information associated with the operator spreading.

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Phase crossover induced by dynamical many-body localization in periodically driven long-range spin systems

Rahaman M., Mori T., Roy A.

Physical Review B （Physical Review B）  109 （ 10 ）  2024年03月

ISSN  24699950

　概要を見る

Dynamical many-body freezing occurs in periodic transverse field-driven integrable quantum spin systems. Under freezing conditions, quantum dynamics causes practically infinite hysteresis in the drive response, maintaining its starting value. We find similar resonant freezing in the Lipkin-Meshkov-Glick (LMG) model. In the LMG, the freezing conditions in the driving field suppresses the heating postulated by the eigenstate thermalization hypothesis (ETH) by inducing dynamical many-body localization, or DMBL. This is in contrast to many-body localization (MBL), which requires disorder to suppress ETH. DMBL has been validated by the inverse participation ratio (IPR) of the quasistationary Floquet modes. Similarly to the TFIM, the LMG exhibits high-frequency localization only at freezing points. IPR localization in the LMG deteriorates with an inverse system size law at lower frequencies, which indicates heating to infinite temperature. Furthermore, adiabatically increasing frequency and amplitude from low values raises the Floquet state IPR in the LMG from nearly zero to unity, indicating a phase crossover. This occurrence enables a future technique to construct an MBL engine in clean systems that can be cycled by adjusting drive parameters only.

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Liouvillian-gap analysis of open quantum many-body systems in the weak dissipation limit

Mori T.

Physical Review B （Physical Review B）  109 （ 6 ）  2024年02月

ISSN  24699950

　概要を見る

Recent experiments have reported that novel physics emerge in open quantum many-body systems due to an interplay of interactions and dissipation, which stimulate theoretical studies of the many-body Lindblad equation. Although the strong dissipation regime receives considerable interest in this context, this work focuses on the weak bulk dissipation. By examining the spectral property of the many-body Lindblad generator for specific models, we find that its spectral gap shows singularity in the weak dissipation limit when the thermodynamic limit is taken first. Based on analytical arguments and numerical calculations, we conjecture that such a singularity is generic in bulk-dissipated quantum many-body systems and is related to the concept of the Ruelle-Pollicott resonance in chaos theory, which determines the timescale of thermalization of an isolated system. This conjecture suggests that the many-body Lindblad equation in the weak dissipation regime contains nontrivial information on intrinsic properties of a quantum many-body system.

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Impact of Measurement Noise on Escaping Saddles in Variational Quantum Algorithms

E Kaminishi, T Mori, M Sugawara, N Yamamoto

arXiv preprint arXiv:2406.09780 2024年

Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound

K Shiraishi, M Nakagawa, T Mori, M Ueda

arXiv preprint arXiv:2404.14067 2024年

Strong Markov dissipation in driven-dissipative quantum systems

T Mori

arXiv preprint arXiv:2404.10195 2024年

Quantum and classical Floquet prethermalization

Ho W.W., Mori T., Abanin D.A., Dalla Torre E.G.

Annals of Physics （Annals of Physics）  454 2023年07月

ISSN  00034916

　概要を見る

Time-periodic (Floquet) driving is a powerful way to control the dynamics of complex systems, which can be used to induce a plethora of new physical phenomena. However, when applied to many-body systems, Floquet driving can also cause heating, and lead to a featureless infinite-temperature state, hindering most useful applications. It is therefore important to find mechanisms to suppress such effects. Floquet prethermalization refers to the phenomenon where many-body systems subject to a high-frequency periodic drive avoid heating for very long times, instead tending to transient states that can host interesting physics. Its key signature is a strong parametric suppression of the heating rate as a function of the driving frequency. Here, we review our present understanding of this phenomenon in both quantum and classical systems, and across various models and methods. In particular, we present rigorous theorems underpinning Floquet prethermalization in quantum spin and fermionic lattice systems and extensions to systems with degrees of freedom that have unbounded local dimension. Further, we briefly describe applications to novel nonequilibrium phases of matter, and recent experiments probing prethermalization with quantum simulators. We close by describing the frontiers of Floquet prethermalization beyond strictly time-periodic drives, including time-quasiperiodic driving and long-lived quasi-conserved quantities enabled by large separation of energy scales.

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Symmetrized Liouvillian Gap in Markovian Open Quantum Systems

Mori T., Shirai T.

Physical Review Letters （Physical Review Letters）  130 （ 23 ）  2023年06月

ISSN  00319007

　概要を見る

Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate toward the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of autocorrelation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always gives a correct upper bound on the decay of the autocorrelation function, but the standard Liouvillian gap does not.

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Floquet States in Open Quantum Systems

Mori T.

Annual Review of Condensed Matter Physics （Annual Review of Condensed Matter Physics）  14   35 - 56 2023年03月

ISSN  19475454

　概要を見る

In Floquet engineering, periodic driving is used to realize novel phases of matter that are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe for obtaining a static effective Hamiltonian. Although many existing works have treated closed systems, it is important to consider the effect of dissipation, which is ubiquitous in nature. Understanding the interplay of periodic driving and dissipation is a fundamental problem of nonequilibrium statistical physics that is receiving growing interest because of the fact that experimental advances have allowed us to engineer dissipation in a controllable manner. In this review, we give a detailed exposition on the formalism of quantum master equations for open Floquet systems and highlight recent work investigating whether equilibrium statistical mechanics applies to Floquet states.

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Heating Rates under Fast Periodic Driving beyond Linear Response

Mori T.

Physical Review Letters （Physical Review Letters）  128 （ 5 ）  2022年02月

ISSN  00319007

　概要を見る

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. In this work, 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. 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.

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Quantum dark solitons in the 1d bose gas: From single to double dark-solitons

Kinjo K., Kaminishi E., Mori T., Sato J., Kanamoto R., Deguchi T.

Universe （Universe）  8 （ 1 ）  2022年01月

　概要を見る

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N − 1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

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Power-Law Escape Rate of SGD

Mori T., Ziyin L., Liu K., Ueda M.

Proceedings of Machine Learning Research （Proceedings of Machine Learning Research）  162   15959 - 15975 2022年

　概要を見る

Stochastic gradient descent (SGD) undergoes complicated multiplicative noise for the mean-square loss. We use this property of SGD noise to derive a stochastic differential equation (SDE) with simpler additive noise by performing a random time change. Using this formalism, we show that the log loss barrier ∆ log L = log[L(θs)/L(θ∗)] between a local minimum θ∗ and a saddle θs determines the escape rate of SGD from the local minimum, contrary to the previous results borrowing from physics that the linear loss barrier ∆L = L(θs) - L(θ∗) decides the escape rate. Our escape-rate formula strongly depends on the typical magnitude h∗ and the number n of the outlier eigenvalues of the Hessian. This result explains an empirical fact that SGD prefers flat minima with low effective dimensions, giving an insight into implicit biases of SGD.

STRENGTH OF MINIBATCH NOISE IN SGD

Ziyin L., Liu K., Mori T., Ueda M.

ICLR 2022 - 10th International Conference on Learning Representations （ICLR 2022 - 10th International Conference on Learning Representations）  2022年

　概要を見る

The noise in stochastic gradient descent (SGD), caused by minibatch sampling, is poorly understood despite its practical importance in deep learning. This work presents the first systematic study of the SGD noise and fluctuations close to a local minimum. We first analyze the SGD noise in linear regression in detail and then derive a general formula for approximating SGD noise in different types of minima. For application, our results (1) provide insight into the stability of training a neural network, (2) suggest that a large learning rate can help generalization by introducing an implicit regularization, (3) explain why the linear learning rate-batchsize scaling law fails at a large learning rate or at a small batchsize and (4) can provide an understanding of how discrete-time nature of SGD affects the recently discovered power-law phenomenon of SGD.

Interplay between depth of neural networks and locality of target functions

T Mori, M Ueda

arXiv preprint arXiv:2201.12082 2022年

Metastability associated with many-body explosion of eigenmode expansion coefficients

Mori T.

Physical Review Research （Physical Review Research）  3 （ 4 ）  2021年12月

ISSN  26431564

　概要を見る

Metastable states in stochastic systems are often characterized by the presence of small eigenvalues in the generator of the stochastic dynamics. We here show that metastability in many-body systems is not necessarily associated with small eigenvalues. Instead, many-body explosion of eigenmode expansion coefficients characterizes slow relaxation, which is demonstrated for two models, interacting particles in a double-well potential and the Fredrickson-Andersen model, the latter of which is a prototypical example of kinetically constrained models studied in glass and jamming transitions. Our results provide insights into slow relaxation and metastability in many-body stochastic systems.

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Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

Mori T., Zhao H., Mintert F., Knolle J., Moessner R.

Physical Review Letters （Physical Review Letters）  127 （ 5 ）  2021年07月

ISSN  00319007

　概要を見る

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)-C ln(ω/g) with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.

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Tensor network approach to thermalization in open quantum many-body systems

Nakano H., Shirai T., Mori T.

Physical Review E （Physical Review E）  103 （ 4 ）  2021年04月

ISSN  24700045

　概要を見る

We investigate the relaxation dynamics of open nonintegrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibbs state with a time-dependent effective temperature in the weak-dissipation and thermodynamic limit.

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