38,108 research outputs found
Chaos in the thermodynamic Bethe ansatz
We investigate the discretized version of the thermodynamic Bethe ansatz
equation for a variety of 1+1 dimensional quantum field theories. By computing
Lyapunov exponents we establish that many systems of this type exhibit chaotic
behaviour, in the sense that their orbits through fixed points are extremely
sensitive with regard to the initial conditions.Comment: 10 pages, Late
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models
A computation scheme for solving elliptic boundary value problems with
axially symmetric confining potentials using different sets of one-parameter
basis functions is presented. The efficiency of the proposed symbolic-numerical
algorithms implemented in Maple is shown by examples of spheroidal quantum dot
models, for which energy spectra and eigenfunctions versus the spheroid aspect
ratio were calculated within the conventional effective mass approximation.
Critical values of the aspect ratio, at which the discrete spectrum of models
with finite-wall potentials is transformed into a continuous one in strong
dimensional quantization regime, were revealed using the exact and adiabatic
classifications.Comment: 6 figures, Submitted to Proc. of The 12th International Workshop on
Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia,
September 5 - 12, 201
Stochastic description for open quantum systems
A linear open quantum system consisting of a harmonic oscillator linearly
coupled to an infinite set of independent harmonic oscillators is considered;
these oscillators have a general spectral density function and are initially in
a Gaussian state. Using the influence functional formalism a formal Langevin
equation can be introduced to describe the system's fully quantum properties
even beyond the semiclassical regime. It is shown that the reduced Wigner
function for the system is exactly the formal distribution function resulting
from averaging both over the initial conditions and the stochastic source of
the formal Langevin equation. The master equation for the reduced density
matrix is then obtained in the same way a Fokker-Planck equation can always be
derived from a Langevin equation characterizing a stochastic process. We also
show that a subclass of quantum correlation functions for the system can be
deduced within the stochastic description provided by the Langevin equation. It
is emphasized that when the system is not Markovian more information can be
extracted from the Langevin equation than from the master equation.Comment: 16 pages, RevTeX, 1 figure (uses epsf.sty). Shortened version.
Partially rewritten to emphasize those aspects which are new. Some references
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A convergent method for linear half-space kinetic equations
We give a unified proof for the well-posedness of a class of linear
half-space equations with general incoming data and construct a Galerkin method
to numerically resolve this type of equations in a systematic way. Our main
strategy in both analysis and numerics includes three steps: adding damping
terms to the original half-space equation, using an inf-sup argument and
even-odd decomposition to establish the well-posedness of the damped equation,
and then recovering solutions to the original half-space equation. The proposed
numerical methods for the damped equation is shown to be quasi-optimal and the
numerical error of approximations to the original equation is controlled by
that of the damped equation. This efficient solution to the half-space problem
is useful for kinetic-fluid coupling simulations
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