arXiv subjects

Wen-ge Wang

Publications and source records attributed to Wen-ge Wang.

At least 19 recordsLinked to original sources

arXiv2026

An ETH-ansatz-motivated environmental-branch approach to open quantum systems

In this paper, a method is developed for the study of a generic small central quantum system, which is locally coupled to an environment as a many-body quantum chaotic system that satisfies the eigenstate thermalization hypothesis (ETH) ansatz. The approach is based on properties of environmental branches of the total system's state, the overlaps of which give the reduced density matrix (RDM) of the central system. To study evolution of the RDM within a finite time period, the period is divided into a series of short intervals, within each of which the RDM is computed by making use of a formal solution to the time evolution of the environmental branches. The expressions thus obtained are simplified by the ETH ansatz and, further, by decay of phase correlations among the environmental branches, the latter of which also originates from chaotic dynamics of the environment. This gives a generic method of deriving master equation. And, as an application, a master equation is derived in a simplest nontrivial case, which predicts a decoherence rate in agreement with that predicted by the random-matrix theory. Furthermore, the Born approximation, which is employed in the ordinary approach to master equation, can be justified within the proposed framework; and a Markovian feature is shown for the RDM's evolution in an effective sense.

quant-ph↗

arXiv2025

Statistical structural properties of many-body chaotic eigenfunctions and applications

In this paper, we employ a semiperturbative theory to study the statistical structural properties of energy eigenfunctions (EFs) in many-body quantum chaotic systems consisting of a central system coupled to an environment. Under certain assumptions, we derive both the average shape and the statistical fluctuations of EFs on the basis formed by the direct product of the energy eigenbases of the system and the environment. Furthermore, we apply our results to two fundamental questions: (i) the properties of the reduced density matrix of the central system in an eigenstate, and (ii) the structure of the off-diagonal smooth function within the framework of the eigenstate thermalization hypothesis. Numerical results are also presented in support of our main findings.

cond-mat.stat-mech↗

arXiv2025

An operator-Weyl-symbol approach to eigenstate thermalization hypothesis

In this letter, by an approach that employs Weyl symbols for operators, a semiclassical theory is developed for the offdiagonal function in the eigenstate thermalization hypothesis, which is for offdiagonal elements $\langle{E_i}\left|O\right|{E_j}\rangle$ of an observable $O$ on the energy basis. It is shown analytically that the matrix of $O$ has a banded structure, possessing a bandwidth $w_b$ that scales linearly with $\hbar$, a phase-space gradient of the classical Hamiltonian, $\langle\left|{\boldsymbol{\nabla }H_{\rm cl}}\right|\rangle$, and an $O$-dependent property. This predicts that the thermalization timescale of a quantum system may be inversely proportional to the phase-space gradient of the Hamiltonian, aligning with intuitions in classical thermalization. This approach also elucidates the origin of a $ρ_{\rm dos}^{-1/2}$-scaling of the offdiagonal function. The analytical predictions are checked numerically in the Lipkin-Meshkov-Glick model.

quant-ph↗

arXiv2025

Observable-manifested correlations in many-body quantum chaotic systems

In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through numerical simulations, we find that for realistic systems, the envelope function of off-diagonal elements of observables exhibits an exponential decay at large $ΔE$, while for randomized models, it tends to be flat. We demonstrate that the correlations of chaotic eigenstates, originating from the delicate structures of Hamiltonians, play a crucial role in the non-trivial structure of the envelope function. Furthermore, we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians. Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from RMT predictions. These understandings offer valuable directions for future research.

nlin.CD↗

arXiv2024

Semiclassical study of diagonal and offdiagonal functions in the eigenstate thermalization hypothesis

The so-called eigenstate thermalization hypothesis (ETH), which has been tested in various manybody models by numerical simulations, supplies a way of understanding eventual thermalization and is believed to be important for understanding processes of thermalization. Two functions play important roles in the application of ETH, one for averaged diagonal elements and the other for the variance of offdiagonal elements of an observable addressed by ETH on the energy basis. For the former function, a semiclassical expression is known of the zeroth order of hbar, while, little is known analytically for the latter. In this paper, a semiclassical expression is derived for the former function, which includes higher-order contributions of hbar. And, a semiclassical approximation is derived for the latter function, under the assumption of negligible correlations among energy eigenfuntions on an action basis. Relevance of the analytical predictions are tested numerically in the Lipkin-Meshkov-Glick model.

cond-mat.stat-mech↗

arXiv2023

Characterization of random features of chaotic eigenfunctions in unperturbed basis

In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that, when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the ``distance'' to quantum chaos. Numerical simulations performed in the LMG model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart.

cond-mat.stat-mech↗

arXiv2022

Preferred basis derived from eigenstate thermalization hypothesis

We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schrödinger evolution of the total system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned. On the eigenbasis of the central system's Hamiltonian, $\frac{1}{2}(m-1)(m+2)$ relations among elements of the averaged RDM are derived. When steady states exist, these relations imply the existence of a preferred basis, given by a renormalized Hamiltonian that includes certain averaged impact of the system-environment interaction. Numerical simulations performed for a qubit coupled to a defect Ising chain conform the analytical predictions.

quant-ph↗

arXiv2022

A geometric structure underlying the interaction Hamiltonian of quantum electrodynamics

In this paper, a simple geometric structure is shown, which underlies the interaction Hamiltonian of quantum electrodynamics. Specifically, eight parts of the interaction Hamiltonian, corresponding to eight basic Feynman diagrams, are found derivable from two operators called fundamental interaction operators (FIOs), with the help of a superoperator that describes vacuum fluctuations. And, the two FIOs have the simple geometric meanings of mapping the state space of an electron-positron pair to that of a photon and the reverse.

physics.gen-ph↗

arXiv2022

A framework for quantum theory of elementary physical entities

A unified framework, which is directly established on the quantum ground, is proposed for elementary physical entities, called \emph{modes} in this paper. The framework is mainly built upon five basic assumptions, which loosely speaking have the following contents. (i) The state space of each mode is given by the direct product of a momentum-state space and a spinor-state space, the latter of which is certain representation space of the $SL(2,C)$ group (a covering group of the Lorentz group); (ii) spinor states of modes have a layer-type structure and modes are either fermionic or bosonic, depending on their helicity properties; (iii) there are three fundamental processes -- free evolution, vacuum fluctuation (emergence or vanishing of a pair of fermionic modes that possess exactly opposite physical properties), and two fundamental interaction processes (change of two fermionic modes into one bosonic mode and the reverse); (iv) vacuum fluctuation happens instantly; and (v) the time evolution operator is constructed from operators, which map state spaces of incoming modes of fundamental processes to those of outgoing modes. The time evolution operator turns out to be a function of quantum fields that are constructed from creation and annihilation operators for free-mode states, whose interaction part has a local feature. As an example, a simple model of modes is studied and is compared with the first-generation part of the standard model (SM). Concerning electroweak interactions, the studied model has a time evolution operator, whose main body is formally similar to that of the SM. Besides, it predicts $\frac 13$ and $\frac 23$ electronic changes for quark-type modes, gives an interpretation to the color degree of freedom, and contains certain modes that behave like dark matters.

physics.gen-ph↗

arXiv2022

Statistical and dynamical properties of the quantum triangle map

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos.

nlin.CD↗

arXiv2020

Quantum Chaos and the Correspondence Principle

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically non-chaotic systems [E.B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)], Here we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.

quant-ph↗

arXiv2020

Closeness of the reduced density matrix of an interacting small system to the Gibbs state

I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form and with a generic interaction strength, when the total system lies in an equilibrium state described by a microcanonical ensemble. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case and the RDM obtained in the uncoupled case. In the eigenbasis of the central system's Hamiltonian, it is shown that the difference between diagonal elements is mainly confined by the ratio of the maximum width of the eigenfunctions of the total system in the uncoupled basis to the width of the microcanonical energy shell; meanwhile, the difference between off-diagonal elements is given by the ratio of certain property of the interaction Hamiltonian to the related level spacing of the central system. As an application, a sufficient condition is given, under which the RDM may have a canonical Gibbs form under system-environment interactions that are not necessarily weak; this Gibbs state usually includes certain averaged effect of the interaction. For central systems that interact locally with many-body quantum chaotic systems, it is shown that the RDM usually has a Gibbs form. I also study the RDM which is computed from a typical state of the total system within an energy shell.

quant-ph↗

arXiv2020

A quantum mechanism underlying the gauge symmetry in quantum electrodynamics

In this paper, a formulation, which is completely established on a quantum ground, is presented for basic contents of quantum electrodynamics (QED). This is done by moving away, from the fundamental level, the assumption that the spin space of bare photons should (effectively) possess the same properties as those of free photons observed experimentally. Within this formulation, bare photons with zero momentum can not be neglected when constructing the photon field; and an explicit expression for the related part of the photon field is derived. When a local gauge transformation is performed on the electron field, this expression predicts a change that turns out to be equal to what the gauge symmetry requires for the gauge field. This gives an explicit mechanism, by which the photon field may change under gauge transformations in QED.

physics.gen-ph↗

arXiv2020

Steady-state relations for a two-level system locally and relatively-strongly coupled to a generic many-body quantum chaotic environment

We study the long-time average of the reduced density matrix (RDM) of a two-level system as the central system, which is locally coupled to a generic many-body quantum chaotic system as the environment, under an overall Schrödinger evolution. The system-environment interaction has a generic form with dissipation. It is shown that, in addition to the exact relations due to unit trace and hermiticity, an approximate relation exists among elements of the averaged RDM computed in the eigenbasis of the central system's Hamiltonian in some interaction regimes. In particular, an explicit expression of the relation is derived for relatively strong interactions, whose strength is above the mean level spacing of the environment, meanwhile, remains small compared with the central system's level spacing. Numerical simulations performed in a model with the environment as a defect Ising chain confirm the analytical predictions.

quant-ph↗

arXiv2019

Similar early growth of out-of-time-ordered correlators in quantum chaotic and integrable Ising chains

Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator (OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this paper, by means of numerical simulations, it is shown that OTOC has similar early growth in two quantum many-body systems, one integrable and one chaotic.

cond-mat.stat-mech↗

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

Symmetries with the same forms as gauge symmetries in the electroweak theory

Within the electroweak theory, it is shown that the form of the total Lagrangian is invariant, under local phase changes of the basis states for leptons and under local changes of the mathematical spaces employed for the description of left-handed spinor states of leptons. In doing this, a contribution from vacuum fluctuations of the leptonic fields, which causes no experimentally-observable effect, is added to the total connection field. Accompanying the above-mentioned changes of basis states, the leptonic and connection fields are found to undergo changes whose forms are similar to $U(1)$ and $SU(2)$ gauge transformations, respectively. These results suggest a simple physical interpretation to gauge symmetries in the electroweak theory.

physics.gen-ph↗

arXiv2019

Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions

We study properties of eigenfunctions of perturbed systems, given on the eigenbases of unperturbed, integrable systems. For a given pair of perturbed and unperturbed systems, with respect to the energy of each perturbed state, the unperturbed basis states can be divided into two groups: one in the classically-allowed region and the other in the classically-forbidden region; correspondingly, the eigenfunction of the perturbed state is also divided into two parts. In the semiclassical limit, it is shown that, making use of components of the eigenfunction in its classically-allowed region, its components in the classically-forbidden region can be written in the form of a convergent perturbation expansion, which is valid for all perturbation strengths.

quant-ph↗