arXiv subjects

Keiji Saito

Publications and source records attributed to Keiji Saito.

At least 73 records · Page 4Linked to original sources

arXiv2018

Thermalization and Heating Dynamics in Open Generic Many-Body Systems

The last decade has witnessed the remarkable progress in our understanding of thermalization in isolated quantum systems. Combining the eigenstate thermalization hypothesis with quantum measurement theory, we extend the framework of quantum thermalization to open many-body systems. A generic many-body system subject to continuous observation is shown to thermalize at a single trajectory level. We show that the nonunitary nature of quantum measurement causes several unique thermalization mechanisms that are unseen in isolated systems. We present numerical evidence for our findings by applying our theory to specific models that can be experimentally realized in atom-cavity systems and with quantum gas microscopy. Our theory provides a general method to determine an effective temperature of quantum many-body systems subject to the Lindblad master equation and thus should be applicable to noisy dynamics or dissipative systems coupled to nonthermal Markovian environments as well as continuously monitored systems. Our work provides yet another insight into why thermodynamics emerges so universally.

cond-mat.stat-mech↗

arXiv2018

Universal First-Passage-Time Distribution of Non-Gaussian Currents

We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any non-equilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.

cond-mat.stat-mech↗

arXiv2018

Uncertainty relations in implementation of unitary operations

The underlying mechanism in the implementation of unitary operation on a system with an external apparatus is studied. We implement the unitary time evolution in the system as a physical phenomenon that results from the interaction between the system and the apparatus. We investigate the fundamental limitation of a good implementation for the desired unitary time evolution. This limitation is manifested in the form of trade-off relations between the accuracy of the implementation and quantum fluctuation of energy in the external apparatus. Our relations clearly show that an accurate unitary operation requires large energy fluctuation inside the apparatus originated from quantum fluctuation.

quant-ph↗

arXiv2018

Heat transport via a local two-state system near thermal equilibrium

Heat transport in spin-boson systems near the thermal equilibrium is systematically investigated. An asymptotically exact expression for the thermal conductance in a low-temperature regime wherein transport is described via a co-tunneling mechanism is derived. This formula predicts the power-law temperature dependence of thermal conductance $\propto T^{2s+1}$ for a thermal environment of spectral density with the exponent $s$. An accurate numerical simulation is performed using the quantum Monte Carlo method, and these predictions are confirmed for arbitrary thermal baths. Our numerical calculation classifies the transport mechanism, and shows that the noninteracting-blip approximation quantitatively describes thermal conductance in the incoherent transport regime.

cond-mat.mes-hall↗

arXiv2018

5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field

We consider a one-dimensional infinite chain of coupled charged har- monic oscillators in a magnetic field with a small stochastic perturbation of order $ε$. We prove that for a space-time scale of order $ε$^{-1} the density of energy distribution (Wigner distribution) evolves according to a linear phonon Boltzmann equation. We also prove that an appropriately scaled limit of solutions of the lin- ear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5/6.

math.PR↗

arXiv2018

Polynomial-time Classical Simulation for One-dimensional Quantum Gibbs States

This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve one-dimensional quantum systems. However, there exists no exact proof that arbitrary one-dimensional quantum Gibbs states can be efficiently solved by a classical computer. Therefore, the aim of this paper is to prove this with the clustering properties for arbitrary finite temperatures $β^{-1}$. We explicitly show an efficient algorithm that approximates the partition function up to an error $ε$ with a computational cost that scales as $n\cdot {\rm poly}(1/ε)$, where the degree of the polynomial depends on $β$ as $e^{O(β)}$. Extending the analysis to higher dimensions at high temperatures, we obtain a weaker result for the computational cost n\cdot (1/ε)^{\log^{D-1} (1/ε)}, where $D$ is the lattice dimension.

quant-ph↗

arXiv2018

Thermal conductivity for coupled charged harmonic oscillators with noise in a magnetic field

We introduce a $d$-dimensional system of charged harmonic oscillators in a magnetic field perturbed by a stochastic dynamics which conserves energy but not momentum. We study the thermal conductivity via the Green-Kubo formula, focusing on the asymptotic behavior of the Green-Kubo integral up to time $t$ (i.e., the integral of the correlation function of the total energy current). We employ the microcanonical measure to calculate the Green-Kubo formula in general dimension $d$ for uniformly charged oscillators. We also develop a method to calculate the Green-Kubo formula with the canonical measure for uniformly and alternately charged oscillators in dimension $1$. We prove that the thermal conductivity diverges in dimension $1$ and $2$ while it remains finite in dimension $3$. The Green--Kubo integral calculated with the microcanonical ensemble diverges as $t^{1/4}$ for uniformly charged oscillators in dimension $1$, while it is known to diverge as $t^{1/2}$ without magnetic field. This is the first rigorous example of the new exponent $1/4$ in the asymptotic behavior for the Green-Kubo integral. We also demonstrate that our result provides the first rigorous example of a diverging thermal conductivity with vanishing sound speed. In addition, employing the canonical measure in the Green-Kubo formula, we prove that the Green-Kubo integral for uniformly and alternately charged oscillators respectively diverges as $t^{1/4}$ and $t^{1/2}$. This means that the exponent depends not only on a non-zero magnetic field but also on the charge structure of oscillators.

math.PR↗

arXiv2018

Speed Limit for Classical Stochastic Processes

Speed limit for classical stochastic Markov processes with discrete states is studied. We find that a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity determines the time scale and plays a crucial role in the inequality. For systems with stationary current, a similar trade-off inequality with the Hatano-Sasa entropy production gives a much better bound on the speed of the state transformation. Our inequalities contain only physically well-defined quantities, and thus the physical picture of these inequalities is clear.

cond-mat.stat-mech↗

arXiv2017

Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport

For classical ballistic transport in a multi-terminal geometry, we derive a universal trade-off relation between total dissipation and the precision, at which particles are extracted from individual reservoirs. Remarkably, this bound becomes significantly weaker in presence of a magnetic field breaking time-reversal symmetry. By working out an explicit model for chiral transport enforced by a strong magnetic field, we show that our bounds are tight. Beyond the classical regime, we find that, in quantum systems far from equilibrium, correlated exchange of particles makes it possible to exponentially reduce the thermodynamic cost of precision.

cond-mat.stat-mech↗

arXiv2017

Heat transport via low-dimensional systems with broken time-reversal symmetry

We consider heat transport through systems with broken time-reversal symmetry. We apply strong magnetic fields to weakly charged particle systems, where the dynamics are dominated by the Lorentz force and spring forces. The standard momentum conservation is not satisfied and the sound wave disappears depending on the charge structure. We introduce an exactly solvable model and demonstrate the appearance of a new universality class. The absence of sound waves affects the relation between equilibrium correlation and the diverging thermal conductivity in the open system.

cond-mat.stat-mech↗

arXiv2017

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without ..... (SEE THE PDF FOR THE REST OF THIS ABSTRACT)

cond-mat.mes-hall↗

arXiv2017

Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems

We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasi-conserved quantity for long time scale. These two general properties lead to intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in quasi-integrable systems.

cond-mat.stat-mech↗

arXiv2016

Universal trade-off relation between power and efficiency for heat engines

For a general thermodynamic system described as a Markov process, we prove a general lower bound for dissipation in terms of the square of the heat current, thus establishing that nonvanishing current inevitably implies dissipation. This leads to a universal trade-off relation between efficiency and power, with which we rigorously prove that a heat engine with nonvanishing power never attains the Carnot efficiency. Our theory applies to systems arbitrarily far from equilibrium, and does not assume any specific symmetry of the model.

cond-mat.stat-mech↗

arXiv2016

Incompatibility between Carnot efficiency and finite power in Markovian dynamics

In Markovian dynamics with the local detailed balance condition, we decompose the total entropy production rate into microscopic transitions. By applying this decomposition to the heat to work conversion process, we rigorously show that the Carnot efficiency implies zero power for any heat engine, even with broken time-reversal symmetry beyond the linear response regime. Moreover, we propose a trade-off relationship between the entropy production rate and the heat flow between the system and bath.

cond-mat.stat-mech↗

arXiv2016

Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment

Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. Quenched disorder is utilized substantially to study such complex systems, whereas its analytical treatment is difficult to handle. We consider finite systems with quenched disorder in order to investigate the effects of sample disorder fluctuations and confinement on single-particle diffusivity. While the system is ergodic in a single disorder realization, the time-averaged mean squared displacement depends on the disorder, i.e., the system is ergodic but non-self-averaging. We find that the inverse Levy distribution is a universal distribution for diffusivity in the sense that it can be applied for arbitrary dimensions. Quantifying the degree of the non-self-averaging effect, we show that fluctuations of single-particle diffusivity far exceed the corresponding annealed theory and also find confinement effects. The relevance for experimental situations is also discussed.

cond-mat.stat-mech↗

arXiv2016

Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In the analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a finite-time scale. Our result reveals a reliable time scale of the validity of the FM expansion, which can be comparable to the experimental time scale. Furthermore, we discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss generic scenario of the prethermalization phenomenon in periodically driven systems.

quant-ph↗

arXiv2015

Energy current cumulants in one-dimensional systems in equilibrium

Recently a remarkable connection has been proposed between the fluctuating hydrodynamic equations of a one-dimensional fluid and the Kardar-Parizi-Zhang (KPZ) equation for interface growth. This connection has been used to relate equilibrium correlation functions of the fluid to KPZ correlation functions. Here we use this connection to compute the exact cumulant generating function for energy current in the fluid system. This leads to exact expressions for all cumulants and in particular to universal results for certain combinations of the cumulants. As examples, we consider two different systems which are expected to be in different universality classes, namely a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Simulations provide excellent confirmation of our theory.

cond-mat.stat-mech↗

arXiv2015

Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations

We introduce a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy. This set-up covers, in particular, periodic micro and nano-heat engines. In a first step, we show how to express total entropy production by properly identified time-independent affinities and currents without making a linear response assumption. In linear response, kinetic coefficients akin to Onsager coefficients can be identified. Specializing to a Fokker-Planck type dynamics, we show that these coefficients can be expressed as a sum of an adiabatic contribution and one reminiscent of a Green-Kubo expression that contains deviations from adiabaticity. Furthermore, we show that the generalized kinetic coefficients fulfill an Onsager-Casimir type symmetry tracing back to microscopic reversibility. This symmetry allows for non-identical off-diagonal coefficients if the driving protocols are not symmetric under time-reversal. We then derive a novel constraint on the kinetic coefficients that is sharper than the second law and provides an efficiency-dependent bound on power. As one consequence, we can prove that the power vanishes at least linearly when approaching Carnot efficiency. We illustrate our general framework by explicitly working out the paradigmatic case of a Brownian heat engine realized by a colloidal particle in a time-dependent harmonic trap subject to a periodic temperature profile. This case study reveals inter alia that our new general bound on power is asymptotically tight.

cond-mat.stat-mech↗