arXiv subjects

Jun Sato

Publications and source records attributed to Jun Sato.

At least 19 recordsLinked to original sources

arXiv2024

Exact analysis of the two-dimensional asymmetric simple exclusion process with attachment and detachment of particles

The asymmetric simple exclusion process (ASEP) is a paradigmatic driven-diffusive system that describes the asymmetric diffusion of particles with hardcore interactions in a lattice. Although the ASEP is known as an exactly solvable model, most exact results are limited to one-dimensional systems. Recently, the exact steady state in the multi-dimensional ASEP has been proposed [1]. The research focused on the situation where the number of particles is conserved. In this paper, we consider the two-dimensional ASEP with the attachment and detachment of particles (ASEP-LK), where particle number conservation is violated. By employing the result in Ref. [1], we construct the exact steady state of the ASEP-LK and reveal its properties through the exact computation of physical quantities.

cond-mat.stat-mech↗

arXiv2024

Exact steady states in the asymmetric simple exclusion process beyond one dimension

The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly solvable model, most of the exact results obtained so far are limited to one-dimensional systems. Here, we construct the exact steady states of the ASEP with closed and periodic boundary conditions in arbitrary dimensions. This is achieved through the concept of transition decomposition, which enables the treatment of the multi-dimensional ASEP as a composite of the one-dimensional ASEPs.

cond-mat.stat-mech↗

arXiv2022

Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation

We show several novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb-Liniger model for the one-dimensional Bose gas with repulsive interactions. We also show an exact finite-size scaling of the fraction of the Bose-Einstein condensation (BEC) in the ground state, which should characterize the quasi-BEC in quantum double dark-soliton states that we assume to occur in the weak coupling regime. First, we show the exact time evolution of the density profile in the quantum state associated with a quantum double dark-soliton by the Bethe ansatz. Secondly, we derive a kind of macroscopic quantum wave-function effectively by exactly evaluating the square amplitude and phase profiles of the matrix element of the field operator between the quantum double dark-soliton states. The profiles are close to those of dark-solitons particularly in the weak-coupling regime. Then, the scattering of two notches in the quantum double dark-soliton state is exactly demonstrated. It is suggested from the above observations that the quasi-BEC should play a significant role in the dynamics of quantum double dark-soliton states. If the condensate fraction is close to 1, the quantum state should be well approximated by the quasi-BEC state where the mean-field picture is valid.

cond-mat.quant-gas↗

arXiv2022

Multi-Quantum Dark Solitons in One-Dimensional Bose Gas

Quantum and classical integrable systems share common mathematical structures, and the phenomena appearing in them are interrelated. Solitons, which universally appear in classical integrable systems, also appear in quantum integrable systems. Here, we consider quantum-classical correspondence in a one-dimensional Bose gas with repulsive delta-function interaction and present quantum states corresponding to multi-dark solitons. Using an exact method, we compute the time evolution of the density profile in the multi-quantum dark soliton states. Localized solitary waves that behave like classical dark solitons are observed in the density profile. We observe collisions of quantum dark solitons and show that they exhibit the properties of classical solitons: stability against scatterings and position shifts due to interactions.

cond-mat.quant-gas↗

arXiv2021

Quantum dark solitons in the 1D Bose gas: From single to double dark-solitons

We study quantum double dark-solitons 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.

cond-mat.quant-gas↗

arXiv2021

Asymmetry-induced delocalization transition in the integrable non-Hermitian spin chain

The emergence of quasiparticles is a universal property in integrable systems. String-type quasiparticles, which are characterized by the string solutions of Bethe equations, play fundamental roles in the analysis of their physics. Through an investigation of the Bethe equations in the asymmetric simple exclusion process, we reveal the existence of string solutions in the presence of non-Hermiticity resulting from asymmetrical hopping. Because of the non-Hermiticity, the string solutions exhibit exotic properties such as the complexification of the center of string solutions and the delocalization of Bethe quantum numbers. In addition, we find the picture of string-type quasiparticles collapses in the strong asymmetry regime. The collapse of string solutions characterizes the transition of eigenstates from bound states to scattering states.

cond-mat.stat-mech↗

arXiv2020

Burgers equation with finite particle correction of the asymmetric simple exclusion process derived from the derivative nonlinear Schr\"{o}dinger equation

We investigate the dynamics of the asymmetric simple exclusion process (ASEP) on a ring. The ASEP is equivalent to the derivative nonlinear Schr\"{o}dinger equation (DNLS), which is integrable quantum field theory, in the continuous limit. We derive the Burgers equation with finite particle correction from the DNLS and numerically confirm that the obtained Burgers equation describes the dynamics of the ASEP at small numbers of particles better than the conventional Burgers equation.

cond-mat.stat-mech↗

arXiv2019

A Biologically Motivated Asymmetric Exclusion Process: interplay of congestion in RNA polymerase traffic and slippage of nascent transcript

We develope a theoretical framework, based on exclusion process, that is motivated by a biological phenomenon called transcript slippage (TS). In this model a discrete lattice represents a DNA strand while each of the particles that hop on it unidirectionally, from site to site, represents a RNA polymerase (RNAP). While walking like a molecular motor along a DNA track in a step-by-step manner, a RNAP simultaneously synthesizes a RNA chain; in each forward step it elongates the nascent RNA molecule by one unit, using the DNA track also as the template. At some special "slippery" position on the DNA, which we represent as a defect on the lattice, a RNAP can lose its grip on the nascent RNA and the latter's consequent slippage results in a final product that is either longer or shorter than the corresponding DNA template. We develope an exclusion model for RNAP traffic where the kinetics of the system at the defect site captures key features of TS events. We demonstrate the interplay of the crowding of RNAPs and TS. A RNAP has to wait at the defect site for longer period in a more congested RNAP traffic, thereby increasing the likelihood of its suffering a larger number of TS events. The qualitative trends of some of our results for a simple special case of our model are consistent with experimental observations. The general theoretical framework presented here will be useful for guiding future experimental queries and for analysis of the experimental data with more detailed versions of the same model.

cond-mat.stat-mech↗

arXiv2018

Quantum-classical correspondence via coherent state in integrable field theory

We consider the problem of quantum-classical correspondence in integrable field theories. We propose a method to construct a field theoretical coherent state, in which the expectation value of the quantum field operator exactly coincides with the classical soliton. We also discuss the time evolution of this quantum state and the instability due to the nonlinearity.

quant-ph↗

arXiv2018

Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain

We derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of $N$ sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of quantum numbers. We derive them analytically for all the complex solutions in the sector, which we call two-string solutions. We show that in a region of $N$ and $Δ$ the number of two-string solutions is by two larger than the number due to the string hypothesis, i.e., an extra pair of two-strings appears. We determine it exactly and also such regions where $m$ two-string solutions collapse for any positive integers $m$. We illustrate the extra and standard two-string solutions numerically. In the sector we show that the string deviations are exponentially small with respect to $N$ if $N$ is large. We argue that for any finite solution of the spin-1/2 XXX chain there is such a solution of the spin-1/2 XXZ chain that has the same quantum numbers in common with the XXX solution.

cond-mat.stat-mech↗

arXiv2018

Relaxation dynamics of closed diffusive systems with infinitesimal Langmuir kinetics

We consider the asymmetric simple exclusion process with Langmuir kinetics in the closed boundary condition. We analytically obtain the exact stationary state and a series of excited states of the system in the limit where Langmuir kinetics is infinitesimally small. Based on this result, we propose an analytical formula for the time evolutions of physical quantities of the system.

cond-mat.stat-mech↗

arXiv2016

Quantum states of dark solitons in the 1D Bose gas

We present a series of quantum states that are characterized by dark solitons of the nonlinear Schrödinger equation (i.e. the Gross-Pitaevskii equation) for the one-dimensional (1D) Bose gas interacting through the repulsive delta-function potentials. The classical solutions satisfy the periodic boundary conditions and we call them periodic dark solitons. Through exact solutions we show corresponding aspects between the states and the solitons in the weak coupling case: the quantum and classical density profiles completely overlap with each other not only at an initial time but also at later times over a long period of time, and they move together with the same speed in time; the matrix element of the bosonic field operator between the quantum states has exactly the same profiles of the square amplitude and the phase as the classical complex scalar field of a periodic dark soliton not only at the initial time but also at later times, and the corresponding profiles move together for a long period of time. We suggest that the corresponding properties hold rigorously in the weak coupling limit. Furthermore, we argue that the lifetime of the dark soliton-like density profile in the quantum state becomes infinitely long as the coupling constant approaches zero, by comparing it with the quantum speed limit time. Thus, we call the quantum states quantum dark soliton states.

cond-mat.quant-gas↗

arXiv2016

Computation of static Heisenberg-chain correlators: Control over length and temperature dependence

We communicate results on correlation functions for the spin-1/2 Heisenberg-chain in two particularly important cases: (a) for the infinite chain at arbitrary finite temperature $T$, and (b) for finite chains of arbitrary length $L$ in the ground-state. In both cases we present explicit formulas expressing the short-range correlators in a range of up to seven lattice sites in terms of a single function $ω$ encoding the dependence of the correlators on $T$ ($L$). These formulas allow us to obtain accurate numerical values for the correlators and derived quantities like the entanglement entropy. By calculating the low $T$ (large $L$) asymptotics of $ω$ we show that the asymptotics of the static correlation functions at any finite distance are $T^2$ ($1/L^2$) terms. We obtain exact and explicit formulas for the coefficients of the leading order terms for up to eight lattice sites.

cond-mat.str-el↗

arXiv2016

Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring

We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no particle in the system. The exact stationary state of this model has been known for the totally asymmetric case. We propose a basis transformation which simplifies the proof of the stationarity of this state and enables the generalization to the partially asymmetric case. Moreover, we construct low-energy excitations and obtain the exact relaxation time.

cond-mat.stat-mech↗

arXiv2015

Crossover temperature of the spin-1/2 XXZ chain with an impurity

We study exactly the effect of an impurity in the interacting quantum spin chain at low temperature by solving the integrable spin-1/2 XXZ periodic chain with an impurity through the algebraic and thermal Bethe ansatz methods. In particular, we investigate how the crossover temperature for the impurity specific heat depends on the impurity parameter, i.e. the coupling of the impurity to other spins, and show that it is consistent with the analytic expression that is obtained by setting the impurity susceptibility to be proportional to the inverse of the crossover temperature. In the model, two types of crossover behavior appear: one from the high-temperature regime to the low-temperature Kondo regime and another from the N-site homogeneous chain to the (N-1)-site chain with a decoupled free impurity spin, with respect to the temperature and the impurity parameter, respectively.

cond-mat.stat-mech↗

arXiv2015

Recurrence time in the quantum dynamics of the 1D Bose gas

Recurrence time is evaluated for some initial quantum states in the one-dimensional Bose gas with repulsive short-range interactions. In the relatively strong and weak coupling cases some different types of initial states show almost complete recurrence and the estimates of recurrence time are proportional to some powers of the system size at least in some range of the system size. They are much longer than in the case of free particles such as 100 times. In the free-bosonic and free-fermionic regimes we evaluate the recurrence time rigorously, which is proportional to the square of the system size. The estimate of recurrence time is given by the order of ten milliseconds in the corresponding experimental systems of cold atoms trapped in one dimension of ten micrometers in length. It is much shorter than the estimate in a generic quantum many-body system, which may be as long as the age of the universe.

cond-mat.quant-gas↗

arXiv2014

Finite-temperature behavior of an impurity in the spin-1/2 XXZ chain

We study the zero- and the finite-temperature behavior of the integrable spin-1/2 XXZ periodic chain with an impurity by the algebraic and thermal Bethe ansatz methods. We evaluate the impurity local magnetization at zero temperature analytically and derive the impurity susceptibility exactly from it. In the graphs of the impurity specific heat versus temperature, we show how the impurity spin becomes more liberated from the bulk many-body effect as the exchange coupling between the impurity spin and other spins decreases, and also that in low temperature it couples strongly to them such as the Kondo effect. Thus, we observe not only the crossover behavior from the high- to the low-temperature regime but also another one from the $N$-site chain to the $(N-1)$-site chain with a free impurity spin. We also show that the estimate of the Wilson ratio at a given low temperature is independent of the impurity parameter if its absolute value is small enough with respect to the temperature, and the universality class is described by the XXZ anisotropy in terms of the dressed charge.

cond-mat.stat-mech↗

arXiv2014

Exact quantum dynamics of yrast states in the finite 1D Bose gas

We demonstrate that the quantum dynamics of yrast states in the one-dimensional (1D) Bose gas gives an illustrative example to equilibration of an isolated quantum many-body system. We first formulate the energy spectrum of yrast states in terms of the dressed energy by applying the method of finite-size corrections. We then review the exact time evolution of quantum states constructed from yrast states shown by the Bethe ansatz. In time evolution the density profile of an initially localized quantum state constructed from yrast states collapses into a flat profile in the case of a large particle number such as N=1000, while recurrence of the localized state occurs in the case of a small particle number such as N=20. We suggest that the dynamical relaxation behavior for the large N case is consistent with the viewpoint of typicality for generic quantum states: the expectation values of local operators valuated in most of quantum states are very close to those of the micro-canonical ensemble.

cond-mat.quant-gas↗