arXiv subjects

Jiao Wang

Publications and source records attributed to Jiao Wang.

At least 37 records · Page 2Linked to original sources

arXiv2020

Calculating the free energy difference by applying the Jarzynski equality to a virtual integrable system

The Jarzynski equality (JE) provides a nonequilibrium method to measure and calculate the free energy difference (FED). Note that if two systems share the same Hamiltonian at two equilibrium states, respectively, they share the same FED between these two equilibrium states as well. Therefore the calculation of the FED of a system may be facilitated by considering instead another virtual system designed to this end. Taking advantage of this flexibility and the JE, we show that by introducing an integrable virtual system, the evolution problem involved in the JE can be solved. As a consequence, FED is expressed in the form of an equilibrium equality, in contrast with the nonequilibrium JE it is based on. Numerically, this result allows FED to be computed by sampling the canonical ensemble directly and the computational cost can be significantly reduced. The effectiveness and efficiency of this scheme are illustrated with numerical studies of several representative model systems.

cond-mat.stat-mech↗

arXiv2020

Self-duality triggered dynamical transition

A basic result about the dynamics of spinless quantum systems is that the Maryland model exhibits dynamical localization in any dimension. Here we implement mathematical spectral theory and numerical experiments to show that this result does not hold, when the 2-dimensional Maryland model is endowed with spin 1/2 -- hereafter dubbed spin-Maryland (SM) model. Instead, in a family of SM models, tuning the (effective) Planck constant drives dynamical localization{delocalization transitions of topological nature. These transitions are triggered by the self-duality, a symmetry generated by some transformation in the parameter -- the inverse Planck constant -- space. This provides significant insights to new dynamical phenomena such as what occur in the spinful quantum kicked rotor.

cond-mat.mes-hall↗

arXiv2020

Inverse Currents in Hamiltonian Coupled Transport

The occurrence of an inverse current, where the sign of the induced current is opposite to the applied force, is a highly counterintuitive phenomenon. We show that inverse currents in coupled transport (ICC) of energy and particle can occur in a one-dimensional interacting Hamiltonian system when its equilibrium state is perturbed by coupled thermodynamic forces. This seemingly paradoxical result is possible due to the self-organization occurring in the system in response to the applied forces.

cond-mat.stat-mech↗

arXiv2020

Thermal rectification in the thermodynamic limit

We show that an increasingly strong thermal rectification effect occurs in the thermodynamic limit in a one-dimensional, graded rotor lattice with nearest-neighboring interactions only. The underlying mechanism is related to the transition from normal to abnormal heat conduction behavior observed in the corresponding homogeneous lattices as the temperature decreases. In contrast and in addition to that by invoking long-range interactions, this finding provides a distinct scenario to make the thermal rectification effect robust.

cond-mat.stat-mech↗

arXiv2019

BigDL: A Distributed Deep Learning Framework for Big Data

This paper presents BigDL (a distributed deep learning framework for Apache Spark), which has been used by a variety of users in the industry for building deep learning applications on production big data platforms. It allows deep learning applications to run on the Apache Hadoop/Spark cluster so as to directly process the production data, and as a part of the end-to-end data analysis pipeline for deployment and management. Unlike existing deep learning frameworks, BigDL implements distributed, data parallel training directly on top of the functional compute model (with copy-on-write and coarse-grained operations) of Spark. We also share real-world experience and "war stories" of users that have adopted BigDL to address their challenges(i.e., how to easily build end-to-end data analysis and deep learning pipelines for their production data).

cs.DC↗

arXiv2019

Thermalization of small quantum systems: From the zeroth law of thermodynamics

Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration of Schrödinger evolution of composite systems, from the perspective of the zeroth law of thermodynamics. Namely, we consider a small quantum system that is brought into contact with a large environmental system; after they have relaxed, they are separated and their temperatures are studied. Our question is under what conditions the small system may have a detectable temperature that is identical with the environmental temperature. This should be a necessary condition for the small quantum system to be thermalized and to have a well-defined temperature. By using a two-level probe quantum system that plays the role of a thermometer, we find that the zeroth law is applicable to quantum chaotic systems, but not to integrable systems.

cond-mat.stat-mech↗

arXiv2019

Onsager symmetry for systems with broken time-reversal symmetry

We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.

cond-mat.stat-mech↗

arXiv2018

Thermodynamic bound on heat to power conversion

In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat to work conversion at a given output power. We show that interacting systems can overcome such bound and saturate, in the thermodynamic limit, the much more favorable linear-response bound. This result is rooted in the possibility for interacting systems to achieve the Carnot efficiency at the thermodynamic limit without delta-energy filtering, so that large efficiencies can be obtained without greatly reducing power.

cond-mat.stat-mech↗

arXiv2018

Hidden thermal structure in Fock space

The emergence of quantum statistical mechanics from individual pure states of closed many-body systems is currently under intensive investigations. While most efforts have been put on the impacts of the direct interaction (i.e., the usual mutual interaction) between particles, here we study systematically and analytically the impacts of the exchange interaction, that arises from the particle indistinguishability. We show that this interaction leads an overwhelming number of Fock states to exhibit a structure, that can be resolved only by observables adjusted according to system's dynamical properties and from which thermal distributions emerge. This hidden thermal structure in Fock space is found to be related to the so-called limit shape of random geometric objects in mathematics. The structure enables us to uncover, for both ideal and nonideal Fermi gases, new mechanisms for the emergence of quantum statistical mechanics from individual eigenstates.

cond-mat.stat-mech↗

arXiv2017

One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System

Self-organization and nonequilibrium phase transitions are well known to occur in two- and three- dimensional dissipative systems. Here, instead, we provide numerical evidence that these phenomena also occur in a one-dimensional Hamiltonian system. To this end, we calculate the heat conductivity by coupling the two ends of our system to two heat baths at different temperatures. It is found that when the temperature difference is smaller than a critical value, the heat conductivity increases with the system size in power law with an exponent considerably smaller than 1. However, as the temperature difference exceeds the critical value, the system's behavior undergoes a transition and the heat conductivity tends to diverge linearly with the system size. Correspondingly, an ordered structure emerges. These findings suggest a new direction for exploring the transport problems in one dimension.

cond-mat.stat-mech↗

arXiv2016

Many-body eigenstate thermalization from one-body quantum chaos: emergent arrow of time

A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, provided one-body quantum chaos is present, as a pure many-body state evolves the arrow of time can emerge, even without interaction or randomness. In times much larger than the Ehrenfest time that signals the breakdown of quantum-classical correspondence, quantum chaotic motion leads to thermal [Fermi-Dirac (FD) or Bose-Einstein (BE)] distributions and thermodynamics in individual eigenstates. Our findings lay dynamical foundation of statistical mechanics and thermodynamics of isolated quantum systems.

quant-ph↗

arXiv2016

Superballistic wavepacket spreading in double kicked rotors

We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor systems, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor systems.

quant-ph↗

arXiv2015

Symmetry and dynamics universality of supermetal in quantum chaos

Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing and finite conductivity, i.e., an "Anderson insulator" and a "metal", respectively. Ballistic motion simulates a perfect crystal with diverging conductivity, i.e., a "supermetal". We analytically find and numerically confirm that, for a large class of chaotic systems, the metal-supermetal dynamics crossover occurs and is universal, determined only by the system's symmetry. Furthermore, we show that the universality of this dynamics crossover is identical to that of eigenfunction and spectral fluctuations described by the random matrix theory.

nlin.CD↗

arXiv2015

Emergence of integer quantum Hall effect from chaos

We present an analytic microscopic theory showing that in a large class of spin-$\frac{1}{2}$ quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum ($h_e$) and the rotor's energy growth rate mimic the `filling fraction' and the `longitudinal conductivity' in conventional IQHE, respectively, and a hidden quantum number is found to mimic the `quantized Hall conductivity'. We show that for an infinite discrete set of critical values of $h_e$, the long-time energy growth rate is universal and of order of unity (`metallic' phase), but otherwise vanishes (`insulating' phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small $h_e$, i.e., it jumps by unity whenever $h_e$ decreases, passing through each critical value. This intriguing phenomenon is not triggered by the like of Landau band filling, well-known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that, for the first time, a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number.Our analytic results are confirmed by numerical simulations.Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics.

nlin.CD↗

arXiv2015

Connection between heat diffusion and heat conduction in one-dimensional systems

Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that for one-dimensional systems, using the indices of particles as the space variable , which has been accepted as a convention, may lead to misleading conclusions. We then show that though in one-dimensional systems there is no general connection between energy diffusion and heat conduction, however, a general connection between heat diffusion and heat conduction may exist. Relaxation behavior of local energy current fluctuations and that of local heat current fluctuations are also studied. We find that they are significantly different, though the global energy current equals the globe heat current.

cond-mat.stat-mech↗

arXiv2015

Normal heat conduction in lattice models with asymmetry harmonic interparticle interactions

We study the thermal conduction behaviors of one-dimensional lattice models with asymmetry harmonic interparticle interactions in this paper. Normal thermal conductivity independent of the system size is observed when the lattice chains are long enough. Because only the harmonic interactions are involved, the result confirms without ambiguous interpretation that the asymmetry plays key role in resulting in the normal thermal conduction in one-dimensional momentum conserving lattices. Both equilibrium and nonequilibrium simulations are performed to support the conclusion.

cond-mat.stat-mech↗

arXiv2015

Key role of asymmetric interactions in low-dimensional heat transport

We study the heat current autocorrelation function (HCAF) in one-dimensional, momentum-conserving lattices. In particular, we explore if there is any relation between the decaying characteristics of the HCAF and asymmetric interparticle interactions. The Lennard-Jones model is intensively investigated in view of its significance to applications. It is found that in wide ranges of parameters, the HCAF decays faster than power-law manners, and in some cases it decays even exponentially. Following the Green-Kubo formula, the fast decay of HCAF implies the convergence of heat conductivity, which is also corroborated by numerical simulations. In addition, with a comparison to the Fermi-Pasta-Ulam-$β$ model of symmetric interaction, the HCAF of the Fermi-Pasta-Ulam-$α$-$β$ model of asymmetric interaction is also investigated. Our study suggests that, in certain ranges of parameters, the decaying behavior of the HCAF is correlated to the asymmetry degree of interaction.

cond-mat.stat-mech↗

arXiv2015

Thermoelectricity of interacting particles: A numerical approach

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to $N>10^4$ particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

cond-mat.stat-mech↗