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Takaaki Monnai

Publications and source records attributed to Takaaki Monnai.

At least 19 recordsLinked to original sources
arXiv2026

Typicality of thermal states in isolated quantum systems corresponds to ubiquity of global minima in wide artificial neural networks

The Neural Tangent Kernel theory theoretically guarantees the existence of global minima of the cost functional in the neighborhood of an arbitrary random initialized parameters in wide artificial neural networks. In this paper, we show that the ubiquity of the global minima directly corresponds to the typicality of pure thermal states in isolated quantum systems by identifying a common underlying mechanism characterized by the restriction to a few observables and the role of a Wishart-type matrix. Moreover, we demonstrate that the increase in distinguishability of the reduced density matrices of typical pure states with subsystem size corresponds to the double descent phenomenon observed by varying the width of layers in finite-width artificial neural networks. Thereby, the threshold for the reduced state become thermal is determined by essentially the same condition as the fitting threshold. In this manner, we reveal a structural correspondence between thermalization in isolated quantum systems and wide neural network.

cond-mat.stat-mech↗
arXiv2023

Kinetic Equality for Susceptibility and Dynamical Activity

We show a general kinetic equality for susceptibilities (KSE) of general fluctuating quantities and for the dynamical activity of nonequilibrium systems described by Markovian master equations. As special limiting cases, KSE reproduces the so-called kinetic uncertainty relation and its multivariate extension. To derive KSE, we also show a kinetic generalization of fluctuation theorem, and an equality for the susceptibility and the observable-frenetic covariance. Hence, KSE provides a master relation of these nonequilibrium kinetic relations.

cond-mat.stat-mech↗
arXiv2023

Universal Lower and Upper Bounds of Efficiency of Heat Engines from Thermodynamic Uncertainty Relation

According to Thermodynamics, the efficiency of a heat engine is upper bounded by Carnot efficiency. For macroscopic systems, the Carnot efficiency is, however, achieved only for quasi static processes. And, considerable attention has been paid to provide general evaluation of the efficiency at a finite speed. Recently, several upper bounds of the efficiency have been derived in the context of the trade-off among the efficiency, power, and other quantities such as the fluctuation of power. Here, we show universal lower and upper bounds of the efficiency from the thermodynamic uncertainty relations for the entropy production and for the heat transfers. The lower bound is characterized by the ratio between the fluctuation of the irreversible entropy production and mean output work. The upper bound of the efficiency is described by a generalized precision of the heat transfers among the working substance, and hot and cold reservoirs. We explicitly derive necessary and sufficient conditions of both the lower and upper bounds in a unified manner in terms of fluctuation theorem. Hence, our result provides an operating principle of the heat engine.

cond-mat.stat-mech↗
arXiv2022

Arbitrary Time Thermodynamic Uncertainty Relation from Fluctuation Theorem

The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer for example for a class of continuous time stochastic processes. However, its extension to general nonequilibrium dynamics is still an unsolved problem. In this Letter, we show TUR for an arbitrary finite time in terms of exchange fluctuation theorem applied to ensemble of copies of the original system by assuming a physical regularity condition for the probability distribution. As a nontrivial practical consequence, we obtain universal scaling relations among the mean and variance of the charge transfer in short time regime. In this manner, we can deepen our understanding on a link between two important rigorous relations, i.e., the fluctuation theorem and the thermodynamic uncertainty relation.

cond-mat.stat-mech↗
arXiv2021

Thermodynamic uncertainty relation in a tilted periodic potential under coarse graining

Recently, some general relations have been studied in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a universal internal relation among the cumulants of currents and the entropy production. In this paper, we give a simple derivation of TUR for thermally fluctuating particle current in a tilted periodic potential from a coarse grained point of view with the use of the transition probabilities. Also, we explore the condition for the bound of TUR to monotonically increase with the affinity.

cond-mat.stat-mech↗
arXiv2019

Relaxation to Gaussian Generalized Gibbs Ensembles in Quadratic Bosonic Systems in the Thermodynamic Limit

Integrable quantum many-body systems are considered to equilibrate to generalized Gibbs ensembles (GGEs) characterized by the expectation values of integrals of motion. We study the dynamics of exactly solvable quadratic bosonic systems in the thermodynamic limit, and show a general mechanism for the relaxation to GGEs, in terms of the diagonal singularity. We show analytically and explicitly that a free bosonic system relaxes from a general (not necessarily Gaussian) initial state under certain physical conditions to a Gaussian GGE. We also show the relaxation to a Gaussian GGE in an exactly solvable coupled system, a harmonic oscillator linearly interacting with bosonic reservoirs.

cond-mat.stat-mech↗
arXiv2018

Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity

The eigenstate thermalization hypothesis (ETH) insists that for nonintegrable systems each energy eigenstate accurately gives microcanonical expectation values for a class of observables. As a mechanism for ETH to hold, we show that the energy eigenstates are superposition of uncountably many quasi eigenstates of operationally defined "time operator", which are thermal for thermodynamic isolated quantum many-body systems and approximately orthogonal in terms of extremely short relaxation time of the fidelity. In this way, our scenario provides a theoretical explanation of ETH.

cond-mat.stat-mech↗
arXiv2017

Quasi adiabatic dynamics of energy eigenstates for solvable quantum system at finite temperature

It is a fundamental problem to characterize the nonequilibrium processes. For a slowly moving one-dimensional potential, we explore the quasi adiabatic dynamics of the initial energy eigenstates for a confined quantum system interacting with a large reservoir. For concreteness, we investigate a dragged harmonic oscillator linearly interacting with an assembly of harmonic oscillators, and explore the deviation from adiabatic processes by rigorously calculating the so-called persistent amplitude. In this way, we also show that the phase of the persistent amplitudes are common both for the ground and excited states.

cond-mat.stat-mech↗
arXiv2016

Typical pure nonequilibrium steady states and irreversibility for quantum transports

It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states (NESS's). We consider a small quantum system coupled to multiple infinite reservoirs. In the long run, the total system reaches a unique NESS. We identify a large Hilbert space from which pure states of the system are to be sampled randomly and show that the typical pure states well describe the NESS. We also point out that the irreversible relaxation to the unique NESS is important to the typicality of the pure NESS's.

cond-mat.stat-mech↗
arXiv2014

Typical Pure Nonequilibrium Steady States

We show that typicality holds for a class of nonequilibrium systems, i.e., nonequilibrium steady states (NESSs): almost all the pure states properly sampled from a certain Hilbert space well represent a NESS and characterize its intrinsic thermal nature. We clarify the relevant Hilbert space from which the pure states are to be sampled, and construct practically all the typical pure NESSs. The scattering approach leads us to the natural extension of the typicality for equilibrium systems. Each pure NESS correctly yields the expectation values of observables given by the standard ensemble approach. It means that we can calculate the expectation values in a NESS with only a single pure NESS. We provide an explicit construction of the typical pure NESS for a model with two reservoirs, and see that it correctly reproduces the Landauer-type formula for the current flowing steadily between the reservoirs.

cond-mat.stat-mech↗
arXiv2014

Spontaneous Symmetry Breaking via Measurement: From Bose-Einstein Condensates to Josephson Effect

Why does spontaneous symmetry breaking occur? Why is a state breaking symmetry realized? We explore an idea that measurement selects such a state even if a system is given in a state respecting the symmetry of the system. We point out that the spectrum of the relevant observable is important, and simply apply the projection postulate for quantum measurement. We first show that this approach correctly describes the well-known interference of Bose-Einstein condensates. We then examine a fermionic system and prove that superconducting states with a definite relative phase are selected by the measurement of the current flowing between two superconductors, eliminating the need to assume the presence of an a priori phase to explain the Josephson effect.

quant-ph↗
arXiv2014

General relaxation time of the fidelity for isolated quantum thermodynamic systems

General evaluation of the relaxation time to equilibrium is usually considered as difficult, since it would strongly depend on the model of interest. In this paper, we provide a generic initial relaxation time of the fidelity for the isolated large systems. The decay of the fidelity is a combination of the Lorentzian and a sinusoidal oscillation. We calculate the relaxation time of the Lorentzian envelop, and the period of the oscillation. Remarkably, these two time scales are the same order when the energy range of the microcanonical state is larger than the thermal fluctuation. Also, the power law decay generally exists for long time regime.

cond-mat.stat-mech↗
arXiv2012

Operational typicality of the nonequilibrium states: a thermodynamic lower bound of the deviation from equilibrium

The typicality of the canonical state shows that majority of the states are indistinguishable from equilibrium, and thus the nonequilibrium states are exceptionally rare in the extremely high-dimensional Hilbert space. On the contrary, we can easily apply an external force acting on the system, and then the actual density matrix quantitatively deviates from the canonical state specified by the system Hamiltonian at each instance. To express how the external forcing amounts to the deviation from equilibrium, we give a universal thermodynamic expression of the lower bound of Hilbert-Schmidt distance between the actual nonequilibrium and corresponding canonical states. The lower bound is expressed only by the amount of forcing and its consequent entropy production rate.

cond-mat.stat-mech↗
arXiv2012

Microscopic reversibility for classical open systems

We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Liouvillian reversible dynamics. It connects the ratio between the probabilities of time forward and reversed trajectories to a degree of the time reversal asymmetry of the final phase space distribution. Indeed, if the final state is in equilibrium, then the forward and reversed net transition probabilities are equal, which gives a generalization of the detailed balance principle. On the other hand, when the external forcing maintains the system out of equilibrium, it expresses an asymmetry for the probabilities of the time forward and reversed trajectories. Especially, it gives a microscopic expression of the heat flowing to a system from a reservoir where the subdynamics seems like a Markovian stochastic process. Also, it turns out that the expression of the microscopic reversibility holds both for the conservative and dissipative dynamics with an arbitrary initial state and external forcing.

cond-mat.stat-mech↗
arXiv2011

Generic evaluation of the relaxation time to equilibrium

We evaluate the relaxation time to equilibrium, and especially show that it is almost independent from the system size for macroscopic isolated quantum systems. It at most polynomially depends on the system size. This estimation holds when the Hamiltonian is non-integrable, the initial deviation of the quantity of interest is of order its spectral norm, and the relaxation process is monotonic.

cond-mat.stat-mech↗
arXiv2011

Microscopic expression of the second law of thermodynamics

The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also shown that the entropy difference between the initial and final states is composed of two positive components. One of the components is expressed as the relative entropy between the initial and final states, while the other is positive due to a dynamical stability called passivity of the canonical ensemble.

physics.class-ph↗
arXiv2011

Microscopic reversibility of quantum open systems

The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to externally perturbed large quantum open systems. The time-dependent external perturbation acts on the subsystem during a transient duration, and subsequently the perturbation is switched off so that the total system would thermalize. We concern with the transition probability for the subsystem between the initial and final eigenstates of the subsystem. In the course of time evolution, the energy is irreversibly exchanged between the subsystem and reservoir. The time reversed probability is given by the reversal of the protocol and the initial ensemble. Microscopic reversibility equates the time forward and reversed probabilities, and therefore appears as a thermodynamic symmetry for open quantum systems.

cond-mat.stat-mech↗