arXiv subjects

Wen-ge Wang

Publications and source records attributed to Wen-ge Wang.

At least 37 records · Page 2Linked to original sources

arXiv2018

Neutrino-mass differences studied in a model with one basic neutrino

In this paper, we propose and study a model, in which there exists only one basic neutrino. Basically, the Lagrangian of the model is obtained from the Lagrangian in the Glashow-Weinberg-Salam electroweak theory by reducing the three flavor neutrinos there to one basic neutrino. In this model, neutrino states with a fixed flavor are interpreted as certain superpositions of states of the basic neutrino and states of the related charged lepton. Neutrino mass states are associated with low-lying eigenstates of the total Hamiltonian. We derive an approximate expression for a ratio of neutrino-mass differences, which gives a value $17$ for the ratio, about half of the experimental result of $33$.

hep-ph↗

arXiv2017

The Fourier heat conduction as a strong kinetic effect

For an one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long, slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our study is illustrated by the 1D diatomic gas model, with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2017

A decoherence interpretation of quantum work for adiabatic processes

In this paper, decoherence is studied for quantum systems undergoing adiabatic processes, which are coupled to huge quantum environments. It is shown that decoherence can happen with respect to a preferred basis given by transient self-Hamiltonian.This result can be used to justify a most-often-used definition of quantum work for a system undergoing an adiabatic process, without resorting to measurement.

quant-ph↗

arXiv2017

Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer

The extent to which a temperature can be appropriately assigned to a small quantum system, as an internal property but not as a property of any large environment, is still an open problem. In this paper, a method is proposed for solving this problem, by which a studied system is coupled to a two-level system (probe) as a microscopic thermometer. For small quantum chaotic systems, we show that a temperature can be determined, the value of which is sensitive to neither the form, location, and strength of the probe-system coupling, nor the Hamiltonian and initial state of the probe. This temperature turns out to have the form of Boltzmann temperature.

cond-mat.stat-mech↗

arXiv2017

Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. An application is given for a relation between transition probabilities.

quant-ph↗

arXiv2016

Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic

We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical unterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.

quant-ph↗

arXiv2014

Signature of existence of a BEC-type state in a dilute gas above the BEC transition temperature

We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence more than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a BEC-type state, some unexplained experimental results [Phys. Rev. A, 71, 043615 (2005)] can be explained.

cond-mat.quant-gas↗

arXiv2014

Complexity and instability of quantum motion near a quantum phase transition

We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can be also used to characterize quantum phase transitions. The non-analytic behavior of this quantity in the neighborhood of a quantum phase transition is illustrated by means of the Dicke model and is compared to two well-known measures of the (in)stability of quantum motion, the quantum Loschmidt echo and the fidelity.

quant-ph↗

arXiv2014

Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations, performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions for the limit of large environment.

quant-ph↗

arXiv2012

Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a 1D Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, in particularly, for perturbation strength in the so-called Fermi-Golden-rule regime.

quant-ph↗

arXiv2012

Scaling behavior for a class of quantum phase transitions

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values $λ_1$ and $λ_2$ of the controlling parameter $λ$, only depend on the ratio $η=(λ_1-λ_c)/(λ_2-λ_c)$, where $λ=λ_c$ at the critical point. Such scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.

quant-ph↗

arXiv2012

Statistical description of small quantum systems beyond weak-coupling limit

An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian. In other cases, the modification may be beyond the mean-field approximation.

quant-ph↗

arXiv2012

Quantum theory for a total system including one internal measuring apparatus

In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a given density operator for the internal measuring apparatus into mixture of pure states may have different physical implications. We use `specified mixed-state description' to call a density operator with a specified decomposition into mixture of pure states. The proposed theory has three basic assumptions, which roughly speaking have the following contents: (i) Physical states of the total system can be associated with vectors in the total Hilbert space; (ii) the dynamical evolution of a state vector obeys Schrödinger equation; and (iii) under a principle of compatible description and certain non-transition condition, a pure-vector description of the total system may imply the existence of certain specified mixed-state description. The principle of compatible description states that different mathematical descriptions for the same physical state of the total system must give consistent predictions for results of measurements performed by the internal measuring apparatus. This principle imposes a restriction to vectors in the Hilbert space and this may effectively break the time-reversal symmetry of Schrödinger equation.

quant-ph↗

arXiv2012

Preferred States of Decoherence under Intermediate System-Environment Coupling

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-environment coupling, PS is known to be the energy eigenstates of the system Hamiltonian or the eigenstates of the system-environment interaction Hamiltonian. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understandings of decoherence and quantum thermalization processes.

quant-ph↗

arXiv2011

Efficiency of dynamical decoupling sequences in presence of pulse errors

For a generic dynamical decoupling sequence employing a single-axis control, we study its efficiency in the presence of small errors in direction of the controlling-pulses. In the case that the corresponding ideal dynamical-decoupling sequence produces good results, the impact of the errors is found to scale as $ξ^2$, with negligible first-order effect, where $ξ$ is the dispersion of the random errors. This analytical prediction is numerically tested in a model, in which the environment is modeled by one qubit coupled to a quantum kicked rotator in chaotic motion. In this model, with periodic pulses applied to the qubit in the environment, it is shown numerically that Uhrig dynamical decoupling is not necessarily better than the bang-bang control.

quant-ph↗

arXiv2010

Semiclassical Approach to Survival Probability at Quantum Phase Transitions

We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival probability for relatively long times in systems with d=1 and an exponential decay in systems with sufficiently large d, where d is the degrees of freedom of the underlying classical dynamics. The semiclassical predictions are checked numerically in four models.

quant-ph↗

arXiv2009

A quantum theory for a total system including a reference system

The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with measurement records given by the values of some reference properties of the RS. In order to describe the total system, we define a frame of reference (FR) as a set of states that can be used to express all other states of the total system. The theory is based on four basic postulates, which have, loosely speaking, the following contents. (i) A reference property of a RS has a definite value and is sufficiently stable in the FR directly related to the reference property. (ii) States of the total system are associated with vectors in the Hilbert space. (iii) Schrödinger equation is the dynamical law in each valid FR. (iv) Under certain condition a property of a system can be regarded as a reference property; vector descriptions of the total system given in different FRs of the same RS may have a probabilistic relationship like in Born's rule.

quant-ph↗

arXiv2008

Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart

We study the stability of a two-component Bose-Einstein condensate (BEC) in the parameter regime in which its classical counterpart has regular motion. The stability is characterized by the fidelity for both the same and different initial states. We study as initial states the Fock states with definite numbers of atoms in each component of the BEC. It is found that for some initial times the two Fock states with all the atoms in the same component of the BEC are stabler than Fock states with atoms distributed in the two components. An experimental scheme is discussed, in which the fidelity can be measured in a direct way.

quant-ph↗