arXiv subjects

Baowen Li

Publications and source records attributed to Baowen Li.

At least 217 records · Page 12Linked to original sources

arXiv2002

Heat conductivity in linear mixing systems

We present analytical and numerical results on the heat conduction in a linear mixing system. In particular we consider a quasi one dimensional channel with triangular scatterers with internal angles irrational multiples of pi and we show that the system obeys Fourier law of heat conduction. Therefore deterministic diffusion and normal heat transport which are usually associated to full hyperbolicity, actually take place in systems without exponential instability.

cond-mat.stat-mech↗

arXiv2002

Fringe Structure in the Phase-Space Dynamics of Atomic Stabilization in An Intense Field

An analytical expression of a Floquet operator, which describes the evolution of a wave packet in combined atomic and an intense laser field,is obtained approximately in the stabilization regime. Both the classical and quantum versions of the Floquet operator are used to study the phase-space dynamics of atomic stabilization, and the 'fringe structure' in the phase-space is clearly demonstrated. Furthermore, we investigate the dynamical mechanism and characters of this striking structure, and find that this structure is very closely related to the classical invariant manifolds.

physics.atm-clus↗

arXiv2002

Electronic properties of the 1D Frenkel-Kontorova model

The energy spectra and quantum diffusion of an electron in a 1D incommensurate Frenkel-Kontorova (FK) model are studied numerically. We found that the spectral and dynamical properties of electron display quite different behaviors in invariance circle regime and in Cantorus regime. In the former case, it is similar to that of the Harper model, whereas in the latter case, it is similar to that of the Fibonacci model. The relationship between spectral and transport properties is discussed.

cond-mat.dis-nn↗

arXiv2002

Finite thermal conductivity in 1D models having zero Lyapunov exponents

Heat conduction in three types of 1D channels are studied. The channels consist of two parallel walls, right triangles as scattering obstacles, and noninteracting particles. The triangles are placed along the walls in three different ways: (a) periodic, (b) disordered in height, and (c) disordered in position. The Lyapunov exponents in all three models are zero because of the flatness of triangle sides. It is found numerically that the temperature gradient can be formed in all three channels, but the Fourier heat law is observed only in two disordered ones. The results show that there might be no direct connection between chaos (in the sense of positive Lyapunov exponent) and the normal thermal conduction.

cond-mat.stat-mech↗

arXiv2001

Correlations of chaotic eigenfunctions: a semiclassical analysis

We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schrödinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.

nlin.CD↗

arXiv2001

Quantum Frenkel-Kontorova Model

This paper gives a review of our recent work on the quantum Frenkel-Kontorova model. Using the squeezed state theory and the quantum Monte Carlo method, we have studied the effects of quantum fluctuations on the Aubry transition and the behavior of the ground state wave function. We found that quantum fluctuations renormalize the sinusoidal standard map to a sawtooth map. Although quantum fluctuations have smeared the Aubry transition, the remnants of this transition are still discernible. The ground state wave function also changes from an extended state to a localized state. The squeezed state results agree very well with those from the Monte Carlo and mean field studies.

cond-mat.stat-mech↗

arXiv2001

Can disorder induce a finite thermal conductivity in 1D lattices?

We study heat conduction in one dimensional mass disordered harmonic and anharmonic lattices. It is found that the thermal conductivity $κ$ of the disordered anharmonic lattice is finite at low temperature, whereas it diverges as $κ\sim N^{0.43}$ at high temperature. Moreover, we demonstrate that a unique nonequilibrium stationary state in the disordered harmonic lattice does not exist at all.

cond-mat.stat-mech↗

arXiv2001

Mode-locking of incommensurate phase by quantum zero point energy in the Frenkel-Kontorova model

In this paper, it is shown that a configuration modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero point energy is taken into account. It is also found that the specific heat for an incommensurate phase shows different parameter-dependence in sliding phase and pinning phase. These findings provide a possible way for experimentalists to verify the phase transition by breaking of analyticity.

cond-mat.stat-mech↗

arXiv2001

Reply to Dhar's comment on "Can disorder induce a finite thermal conductivity in 1D lattices"

In his comment, Dhar (cond-mat/0106349) claims that the existence and uniqueness of a nonequilibrium stationary state has been proved by Lebowitz et al. We should point out that our observation does not contradict the proof. They have only proved that when a (mass) disordered harmonic chain is placed in contact with stochastic reservoirs of the Langevin type, a nonequilibrium stationary state can be reached. However, they didn't prove the existence and uniqueness of the nonequilibrium stationary state for the general case, namely, when the chain is in contact with general thermostated reservoirs (see Bonneto et al. math-ph/0002052).

cond-mat.stat-mech↗

arXiv2000

Universal statistics of wave functions in chaotic and disordered systems

We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of Lorentzian distribution.

chao-dyn↗

arXiv2000

Disturbance spreading in incommensurate and quasiperiodic systems

The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances $σ^2(t)$ of atom displacements depends on the initial condition. For the initial condition with nonzero momentum, $σ^2(t)$ goes as $t^α$ with $α=1$ and 0 for incommensurate Frenkel-Kontorova (FK) model at $V$ below and above $V_c$ respectively; and $α=1$ for uniform, quasiperiodic and random chains. It is also found that $α=1-β$ with $β$ the exponent of distribution function of frequency at zero frequency, i.e., $ρ(ω)\sim ω^β$ (as $ω\to 0$). For the initial condition with zero momentum, $α=0$ for all systems studied. The underlying physical meaning of this diffusive behavior is discussed.

cond-mat.stat-mech↗

arXiv2000

Heat conduction in one dimensional nonintegrable systems

Two classes of 1D nonintegrable systems represented by the Fermi-Pasta-Ulam (FPU) model and the discrete $ϕ^4$ model are studied to seek a generic mechanism of energy transport in microscopic level sustaining macroscopic behaviors. The results enable us to understand why the class represented by the $ϕ^4$ model has a normal thermal conductivity and the class represented by the FPU model does not even though the temperature gradient can be established.

cond-mat↗

arXiv1999

Numerical accuracy of Bogomolny's semiclassical quantization scheme in quantum billiards

We use the semiclassical quantization scheme of Bogomolny to calculate eigenvalues of the Lima\c con quantum billiard corresponding to a conformal map of the circle billiard. We use the entire billiard boundary as the chosen surface of section (SOS) and use a finite approximation for the transfer operator in coordinate space. Computation of the eigenvalues of this matrix combined with a quantization condition, determines a set of semiclassical eigenvalues which are compared with those obtained by solving the Schrödinger equation. The classical dynamics of this billiard system undergoes a smooth transition from integrable (circle) to completely chaotic motion, thus providing a test of Bogomolny's semiclassical method in coordinate space in terms of the morphology of the wavefunction. We analyze the results for billiards which exhibit both soft and hard chaos.

chao-dyn↗

arXiv1999

Ground state wavefunction of the quantum Frenkel-Kontorova model

The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wavefunction crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.

cond-mat↗

arXiv1999

Quantum chaos of a kicked particle in a 1D infinite square potential well

We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion coefficient D in the regime increases with the perturbative strength K giving a scaling $D \propto K^{2.5}$, and in the large K regime D goes as K^2. Quantum mechanically, we observe that the level spacing statistics of the quasi eigenenergies changes from Poisson to Wigner distribution as the kick strength increases. The quasi eigenstates show power-law localization in the small K region, which become extended one at large K. Possible experimental realization of this model is also discussed.

chao-dyn↗

arXiv1999

Wave transmission, phonon localization and heat conduction of 1D Frenkel-Kontorova chain

We study the transmission coefficient of a plane wave through a 1D finite quasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in an infinite uniform harmonic chain. By varying the mass of atoms in the infinite uniform chain, we obtain the transmission coefficients for {\it all} eigenfrequencies. The phonon localization of the incommensurated FK chain is also studied in terms of the transmission coefficients and the Thouless exponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chain at low temperature is calculated. It is found that the stationary heat flux $J(N)\sim N^α$, and $α$ depends on the strength of the external potential.

cond-mat.stat-mech↗

arXiv1998

Nonadiabatic Geometric Phase and Hannay Angle: A Squeezed State Approach

The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. A class of cyclic states are expressed as a superposition of an infinte number of squeezed states. Then, their geometric phases are obtained explicitly and found to be $-(n+1/2)$ times the classical nonadiabatic Hannay angle. It is shown that the analysis based on squeezed state approach provide a clear picture of the geometric meaning of the quantal phase.

cond-mat↗

arXiv1998

Non-Monotone Characteristic of Spectral Statistics in the Transition between Poisson and Gauss

We have computed the spectral number variances of an extended random matrix ensemble predicted by Guhr's supersymmetry formula, showing a non-monotone increase of the curves that arises from an "overshoot" of the two-level correlation function above unity. On the basis of the most general form of $N$-level joint distribution that meets sound probabilistic conditions on matrix spaces, the above characteristic may be attributed to the {\it attractiveness} of the pair potential in long range($E >$ Thouless energy) of the underlying level gas. The approach of level dynamics indicates that the result is "anti-screening" of the level repulsion in short-range statistics of the usual random matrix prediction until the joint level distribution undergoes a phase transition (the Anderson transition).

cond-mat↗