arXiv subjects

Keiji Saito

Publications and source records attributed to Keiji Saito.

At least 55 records · Page 3Linked to original sources

arXiv2021

Revisiting the Mazur bound and the Suzuki equality

Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

cond-mat.stat-mech↗

arXiv2020

Delta-T noise in the Kondo regime

We study the delta-T noise in the Kondo regime, which implies the charge current noise under the temperature bias for the SU(2) Kondo quantum dot. We propose an experimentally measurable quantity to quantify the low-temperature properties in the delta-T noise: $S_{\ell}=S(T_{\mathrm{L}},T_{\mathrm{R}}) - (1/2)[S(T_{\mathrm{L}},T_{\mathrm{L}}) + S(T_{\mathrm{R}},T_{\mathrm{R}})]$, which yields the shot noise expression in the noninteracting limit. We calculate this quantity for the SU(2) Kondo quantum dot in the particle-hole symmetric case. We found that the $S_{\ell}$ exhibits qualitatively the same behavior in both the electrochemical potential biased case and the temperature biased case. The quantitative difference appears as a difference of the coefficients of the noises, which reflects the difference of the Fermi distribution function: electrochemical potential biased or temperature biased.

cond-mat.mes-hall↗

arXiv2020

Area law of non-critical ground states in 1D long-range interacting systems

The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state. Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems. However, the area law for long-range interacting systems is still elusive, as the long-range interaction results in correlation patterns similar to those in critical phases. Here, we show that for generic non-critical one-dimensional ground states with locally bounded Hamiltonians, the area law robustly holds without any corrections, even under long-range interactions. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm.

quant-ph↗

arXiv2020

Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interaction

This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body observables is restricted by a Gaussian concentration bound (or Chernoff--Hoeffding inequality) above some threshold temperature. This bound is then derived for arbitrary Gibbs states of systems that include long-range interactions Secondly, we establish a quantitative relationship between the concentration bound of the Gibbs state and the equivalence of canonical and micro-canonical ensembles. We then evaluate the difference in the averages of thermodynamic properties between the canonical and the micro-canonical ensembles. Under the assumption of the Gaussian concentration bound on the canonical ensemble, the difference between the ensemble descriptions is upper-bounded by $\left[n^{-1} \log (n^{3/2}Δ^{-1})\right]^{1/2}$ with $n$ being the system size and $Δ$ being the width of the energy shell of the micro-canonical ensemble This limit gives a non-trivial upper bound \textit{exponentially small energy width} with respect to the system size. By combining these two results, we prove the ensemble equivalence as well as the weak eigenstate thermalization in arbitrary long-range-interacting systems above a threshold temperature.

cond-mat.stat-mech↗

arXiv2020

Strictly linear light cones in long-range interacting systems of arbitrary dimensions

In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as $R^{-α}$ with distance $R$. We prove the existence of the linear light cone for $α>2D+1$ ($D$: the spatial dimension), where we obtain the Lieb--Robinson bound as $\|[O_i(t),O_j]\|\lesssim{t}^{2D+1}(R-\bar{v}t)^{-α}$ with $\bar{v}=\mathcal{O}(1)$ for two arbitrary operators $O_i$ and $O_j$ separated by a distance $R$. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for $α<2D+1$. In the regime of $α>2D+1$, our result characterizes the best general constraints on the information spreading.

quant-ph↗

arXiv2020

Eigenstate thermalization from the clustering property of correlation

The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in non-critical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting the clustering property. We investigate two regimes, namely, regimes of high and low density of states corresponding to high and low energy regimes, respectively. We show that the clustering property is connected to several properties on the eigenstate thermalization through the density of states. Remarkably, the eigenstate thermalization is obtained in the low-energy regime with sparse density of states, which is typically seen in gapped systems. For the high-energy regime, we demonstrate the ensemble equivalence between microcanonical and canonical ensembles even for subexponentially small energy shell with respect to the system size, which eventually leads to the weak version of eigenstate thermalization.

cond-mat.stat-mech↗

arXiv2020

Energy current correlation in solvable long-range interacting systems

We consider heat transfer in one-dimensional systems with long-range interactions. It is known that typical short-range interacting systems shows anomalous behavior in heat transport when total momentum is conserved, whereas momentum-nonconserving systems do not exhibit anomaly. In this study, we focus on the effect of long-range interaction. We propose an exactly solvable model that reduces to the so-called momentum-exchange model in the short-range interaction limit. We exactly calculate the asymptotic time-decay in the energy current correlation function, which is related to the thermal conductivity via the Green--Kubo formula. From the time-decay of the current correlation, we show three qualitatively crucial results. First, the anomalous exponent in the time-decay {\it continuously} changes as a function of the index of the long-range interaction. Second, there is a regime where the current correlation diverges as increasing the system size with fixed time, and hence the exponent of the time-decay cannot be defined. Third, even momentum-nonconserving systems can show the anomalous exponent indicating anomalous heat transport. Higher-dimensions are also considered, and we found that long-range interaction can induce anomalous exponent even in the three-dimensional systems.

cond-mat.stat-mech↗

arXiv2020

Speed limit for open systems coupled to general environments

In this study, we investigate the bound on the speed of state transformation in the quantum and classical systems that are coupled to general environment with arbitrary coupling interactions. We show that a Mandelstam-Tamm type speed limit exists and energy fluctuation still plays a crucial role in this speed limit inequality for open quantum systems. The energy fluctuation of the target system in addition to the coupling to the environment is key in the inequality. We also present the classical version of the speed limit for open systems. As potential applications of the proposed speed limit expression, we discuss the fundamental limitation of the state change in quantum cyclic engines and the equilibriation time required for the thermalization phenomena of isolated quantum systems.

cond-mat.stat-mech↗

arXiv2020

Trace of anomalous diffusion in a biased quenched trap model

Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drift or the diffusion coefficient remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes zero when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.

cond-mat.stat-mech↗

arXiv2019

Many-body scar state intrinsic to periodically driven system: Rigorous results

The violation of the Floquet version of eigenstate thermalization hypothesis is systematically discussed with realistic Hamiltonians. Our model is based on the PXP type interactions without disorder. We exactly prove the existence of many-body scar states in the Floquet eigenstates, by showing the explicit expressions of the wave functions. Using the underlying physical mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.

cond-mat.stat-mech↗

arXiv2019

Coherence cost for violating conservation laws

Nature imposes many restrictions on the operations that we perform. Many of these restrictions can be interpreted in terms of {\it resource} required to realize the operations. Classifying required resource for different types of operations and determining the amount of resource are the crucial subjects in physics. Among many types of operations, a unitary operation is one of the most fundamental operation that has been studied for long time in terms of the resource implicitly and explicitly. Yet, it is a long standing open problem to identify the resource and to clarify the necessary and sufficient amount of resource for implementing a general unitary operation under conservation laws. In this paper, we provide a solution to this open problem. We derive an asymptotically exact equality that clarifies the necessary and sufficient amount of quantum coherence as a resource to implement arbitrary unitary operation within a desired error. In this equality, the required coherence cost is asymptotically expressed with the implementation error and the degree of violation of conservation law in the desired unitary operation. We also discuss the underlying physics in several physical situations from the viewpoint of coherence cost based on the equality. This work does not only provide a solution to a long-standing problem on the unitary control, but also clarifies the key question of the resource theory of the quantum channels in the region of resource theory of asymmetry, for the case of unitary channels.

quant-ph↗

arXiv2019

Thermodynamic Geometry of Microscopic Heat Engines

We develop a geometric framework to describe the thermodynamics of microscopic heat engines driven by slow periodic temperature variations and modulations of a mechanical control parameter. Covering both the classical and the quantum regime, our approach reveals a universal trade-off relation between efficiency and power that follows solely from geometric arguments and holds for any thermodynamically consistent microdynamics. Focusing on Lindblad dynamics, we derive a second bound showing that coherence as a genuine quantum effect inevitably reduces the performance of slow engine cycles regardless of the driving amplitudes. To demonstrate the practical applicability of our results, we work out the example of a single-qubit heat engine, which lies within the range of current solid-state technologies.

cond-mat.stat-mech↗

arXiv2019

Exact Results for First-Passage-Time Statistics in Biased Quenched Trap Models

We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period $L$. FPT statistics are crucially affected by the disorder realization. In the large-$L$ limit, we obtain exact formulae for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulae are still useful for nonperiodic heterogeneous environments; i.e, the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.

cond-mat.stat-mech↗

arXiv2019

Thermoelectric coefficients and the figure of merit for large open quantum dots

We consider the thermoelectric response of chaotic or disordered quantum dots in the limit of phase-coherent transport, statistically described by random matrix theory. We calculate the full distribution of the thermoelectric coefficients (Seebeck $S$ and Peltier $Π$), and the thermoelectric figure of merit $ZT$, for large open dots at arbitrary temperature and external magnetic field, when the number of modes in the left and right leads ($N_{\rm L}$ and $N_{\rm R}$) are large. Our results show that the thermoelectric coefficients and $ZT$ are maximal when the temperature is half the Thouless energy, and the magnetic field is negligible. They remain small, even at their maximum, but they exhibit a type of universality at all temperatures, in which they do not depend on the asymmetry between the left and right leads $(N_{\rm L}-N_{\rm R})$, even though they depend on $(N_{\rm L}+N_{\rm R})$.

cond-mat.mes-hall↗

arXiv2019

Non-self-averaging behaviors and ergodicity in quenched trap model with finite system size

Tracking tracer particles in heterogeneous environments plays an important role in unraveling the material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of such disorder realizations sometimes become considerably large. When we investigate the sample-to-sample fluctuations, fundamental averaging procedures are a thermal average for a single disorder realization and the disorder average for different disorder realizations. Here, we report on non-self-averaging phenomena in quenched trap models with finite system sizes, where we consider the periodic and the reflecting boundary conditions. Sample-to-sample fluctuations of diffusivity greatly exceeds trajectory-to-trajectory fluctuations of diffusivity in the corresponding annealed model. For a single disorder realization, the time-averaged mean square displacement and position-dependent observables converge to constants with the aid of the existence of the equilibrium distribution. This is a manifestation of ergodicity. As a result, the time-averaged quantities do not depend on the initial condition nor on the thermal histories but depend crucially on the disorder realization.

cond-mat.stat-mech↗

arXiv2018

Speed limit for open quantum systems

We study the quantum speed limit for open quantum systems described by the Lindblad master equation. The obtained inequality shows a trade-off relation between the operation time and the physical quantities such as the energy fluctuation and the entropy production. We further identify a quantity characterizing the speed of the state transformation, which appears only when we consider the open system dynamics in the quantum regime. When the thermal relaxation is dominant compared to the unitary dynamics of the system, we show that this quantity is approximated by the energy fluctuation of the counter-diabatic Hamiltonian which is used as a control field in the shortcuts to adiabaticity protocol. We discuss the physical meaning of the obtained quantum speed limit and try to give better intuition about the speed in open quantum systems.

quant-ph↗

arXiv2018

Nernst-like Effect in a Flexible Chain

We investigate heat transport via a charged flexible chain in the presence of magnetic fields. We focus on the Nernst-like effect, where the average positions of particles deviate in the perpendicular direction to the heat flow. This phenomenon is induced by the nonlinear dynamics as well as nonequilibrium state. We develop a linear response formalism to derive a thermodynamic force which induces the Nernst-like effect, and show that the phenomenon is quantitatively explained. We also discuss the inverse effect, where an external ac-driving force induces finite net heat current in the homogeneous system attached to heat baths with the same temperature.

cond-mat.stat-mech↗

arXiv2018

Fundamental relation between entropy production and heat current

We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes. We establish the fact that quick energy exchange inevitably induces large entropy production in a quantitative form. More specifically, we prove two inequalities on instantaneous quantities: One is applicable to general Markov processes induced by heat baths, and the other is applicable only to systems with the local detailed-balance condition but is stronger than the former one. We demonstrate the physical meaning of our result by applying to some specific setups. In particular, we show that our inequalities are tight in the linear response regime.

cond-mat.stat-mech↗