arXiv subjects

Takashi Mori

Publications and source records attributed to Takashi Mori.

At least 19 recordsLinked to original sources

arXiv2026

Time-Uniform Error Bound for Temporal Coarse Graining in Markovian Open Quantum Systems

Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov quantum master equation (e.g., the Redfield equation). Establishing rigorous error bounds for these approximations is of fundamental and practical importance. However, existing bounds face two major limitations: they are highly specific to individual methods, and, more critically, they diverge in the long-time limit, ensuring the accuracy of the derived GKSL generator only in short-time regimes. In this Letter, we resolve both issues by deriving a unified, rigorous error bound for a general class of approximation methods -- termed temporal coarse graining -- that encompasses all aforementioned schemes. Crucially, our error bound is time-uniform. This guarantees that GKSL generators obtained via temporal coarse graining remain accurate for arbitrarily long times, provided the dissipation timescale is significantly longer than the bath correlation timescale.

cond-mat.stat-mech↗

arXiv2026

Quasi-Strong-Strong Beam-Beam Modeling of Bootstrapping Injection in FCC-ee

The FCC-ee is designed to operate with exceptionally strong beam--beam interactions, making continuous injection a critical and non-trivial aspect of its operation. During the injection process, an unavoidable charge imbalance between the two colliding beams leads to asymmetric beam--beam forces, potentially compromising transverse stability. In this paper, we introduce a quasi-strong-strong (QSS) beam--beam scheme, implemented in the SAD simulation framework. The method preserves a self-consistent beam--beam lens by coupling paired weak--strong simulations, while avoiding the computational cost of full strong--strong tracking. The injection process is modeled as a gradual increase of the stored bunch population, allowing the isolated study of beam--beam--driven optics deformation under charge imbalance. Using the QSS approach, we investigate the feasibility of bootstrapping injection in the Z, W, and H operating modes of FCC-ee. Stable injection paths up to the nominal bunch population are identified in the W and H modes. In contrast, in the explored parameter region, the Z mode exhibits saturation of the stored population below the nominal value.

physics.acc-ph↗

arXiv2025

Error bounds on the universal Lindblad equation in the thermodynamic limit

It is a central problem in various fields of physics to elucidate the behavior of quantum many-body systems subjected to bulk dissipation. In this context, several microscopic derivations of the Lindblad quantum master equation for many-body systems have been proposed so far. Among them, the universal Lindblad equation derived by Nathan and Rudner is fascinating because it has the desired locality and its derivation seems to rely solely on the assumption that the bath correlation time is much shorter than the dissipation time, which is the case in the weak-coupling limit or the singular-coupling limit. However, it remains elusive whether errors from several approximations in deriving the universal Lindblad equation remain small during the time evolution in the thermodynamic limit. Here, rigorous error bounds on the time evolution of a local quantity are given, and it is shown that, under the assumption of accelerated dissipation in bulk-dissipated systems, those errors vanish in the weak-coupling limit or the singular-coupling limit after taking the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2025

Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems

We derive a thermodynamically consistent quantum master equation that satisfies locality for quadratic systems coupled to independent and identical baths at each site. We show that the quasi-local Redfield equation coincides exactly with the Davies equation, which satisfies the detailed-balance condition, due to cancellation of quantum coherence generated by each bath. This derivation does not rely on the secular approximation, which fails in systems with vanishing energy-level spacings. We discuss generalizations of our result to slowly driven quadratic systems and generic quantum many-body systems. Our result paves the way to a thermodynamically consistent description of quantum many-body systems.

quant-ph↗

arXiv2025

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

The local Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) quantum master equation is a powerful tool for the study of open quantum many-body systems. However, its microscopic derivation applicable to many-body systems is available only in limited cases of weak internal couplings, and it has yet to be fully understood under what microscopic conditions the local GKSL equation is valid. We derive the local GKSL equation on the basis of the Lieb-Robinson bound, which provides an upper bound of the propagation of information in quantum many-body systems. We numerically test the validity of the derived local GKSL equation for a one-dimensional tight-binding fermion chain.

quant-ph↗

arXiv2025

Out-of-time-order correlator computation based on discrete truncated Wigner approximation

We propose a method based on the discrete truncated Wigner approximation (DTWA) for computing out-of-time-order correlators. This method is applied to long-range interacting quantum spin systems where the interactions decay as a power law with distance. As a demonstration, we use a squared commutator of local operators and its higher-order extensions that describe quantum information scrambling under Hamilton dynamics. Our results reveal that the DTWA method accurately reproduces the exact dynamics of the average spreading of quantum information (i.e., the squared commutator) across all time regimes in strongly long-range interacting systems. We also identify limitations in the DTWA method when capturing dynamics in weakly long-range interacting systems and the fastest spreading of quantum information. Then we apply the DTWA method to investigate the system-size dependence of the scrambling time in strongly long-range interacting systems. We reveal that the scaling behavior of the scrambling time for large system sizes qualitatively changes depending on the interaction range. This work provides and demonstrates a new technique to study scrambling dynamics in long-range interacting quantum spin systems.

cond-mat.stat-mech↗

arXiv2025

Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries

It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system in a periodic boundary condition, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to non-trivial phase, defined from the spectrum in open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.

cond-mat.stat-mech↗

arXiv2024

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

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.

cond-mat.stat-mech↗

arXiv2024

Impact of Measurement Noise on Escaping Saddles in Variational Quantum Algorithms

Stochastic gradient descent (SGD) is a frequently used optimization technique in classical machine learning and Variational Quantum Eigensolver (VQE). For the implementation of VQE on quantum hardware, the results are always affected by measurement shot noise. However, there are many unknowns about the structure and properties of the measurement noise in VQE and how it contributes to the optimization. In this work, we analyze the effect of measurement noise to the optimization dynamics. Especially, we focus on escaping from saddle points in the loss landscape, which is crucial in the minimization of the non-convex loss function. We find that the escape time (1) decreases as the measurement noise increases in a power-law fashion and (2) is expressed as a function of $η/N_s$ where $η$ is the learning rate and $N_s$ is the number of measurements. The latter means that the escape time is approximately constant when we vary $η$ and $N_s$ with the ratio $η/N_s$ held fixed. This scaling behavior is well explained by the stochastic differential equation (SDE) that is obtained by the continuous-time approximation of the discrete-time SGD. According to the SDE, $η/N_s$ is interpreted as the variance of measurement shot noise. This result tells us that we can learn about the optimization dynamics in VQE from the analysis based on the continuous-time SDE, which is theoretically simpler than the original discrete-time SGD.

quant-ph↗

arXiv2024

Strong Markov dissipation in driven-dissipative quantum systems

The Lindblad equation, which describes Markovian quantum dynamics under dissipation, is usually derived under the weak system-bath coupling assumption. Strong system-bath coupling often leads to non-Markov evolution. The singular-coupling limit is known as an exception: it yields a Lindblad equation with an arbitrary strength of dissipation. However, the singular-coupling limit requires high-temperature limit of the bath, and hence the system ends up in a trivial infinite-temperature state, which is not desirable in the context of quantum control. In this work, it is shown that we can derive a Markovian Lindblad equation for an arbitrary strength of the system-bath coupling by considering a new scaling limit that is called the singular-driving limit, which combines the singular-coupling limit and fast periodic driving. In contrast to the standard singular-coupling limit, an interplay between dissipation and periodic driving results in a nontrivial steady state.

cond-mat.stat-mech↗

arXiv2024

Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems

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.

cond-mat.stat-mech↗

arXiv2024

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

Recent experiments have reported that novel physics emerge in open quantum many-body sys- tems 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 in- terest 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.

cond-mat.stat-mech↗

arXiv2022

Symmetrized Liouvillian Gap in Markovian Open Quantum Systems

Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards 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 auto-correlation 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 give a correct upper bound on the decay of the auto-correlation function, but the standard Liouvillian gap does not.

cond-mat.stat-mech↗

arXiv2022

Quantum and classical Floquet prethermalization

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, 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.

cond-mat.stat-mech↗

arXiv2022

Floquet States in Open Quantum Systems

In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of 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 interplay of periodic driving and dissipation is not only a fundamental problem of nonequilibrium statistical physics, but also 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 works investigating whether equilibrium statistical mechanics applies to Floquet states.

cond-mat.stat-mech↗

arXiv2022

Strength of Minibatch Noise in SGD

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.

cs.LG↗

arXiv2022

Power-law escape rate of SGD

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 $Δ\log L=\log[L(θ^s)/L(θ^*)]$ between a local minimum $θ^*$ and a saddle $θ^s$ determines the escape rate of SGD from the local minimum, contrary to the previous results borrowing from physics that the linear loss barrier $ΔL=L(θ^s)-L(θ^*)$ 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.

cs.LG↗

arXiv2022

Interplay between depth of neural networks and locality of target functions

It has been recognized that heavily overparameterized deep neural networks (DNNs) exhibit surprisingly good generalization performance in various machine-learning tasks. Although benefits of depth have been investigated from different perspectives such as the approximation theory and the statistical learning theory, existing theories do not adequately explain the empirical success of overparameterized DNNs. In this work, we report a remarkable interplay between depth and locality of a target function. We introduce $k$-local and $k$-global functions, and find that depth is beneficial for learning local functions but detrimental to learning global functions. This interplay is not properly captured by the neural tangent kernel, which describes an infinitely wide neural network within the lazy learning regime.

cs.LG↗