31 research outputs found
Complexity, Tunneling and Geometrical Symmetry
It is demonstrated in the context of the simple one-dimensional example of a
barrier in an infinite well, that highly complex behavior of the time evolution
of a wave function is associated with the almost degeneracy of levels in the
process of tunneling. Degenerate conditions are obtained by shifting the
position of the barrier. The complexity strength depends on the number of
almost degenerate levels which depend on geometrical symmetry. The presence of
complex behavior is studied to establish correlation with spectral degeneracy.Comment: 9 revtex pages, 6 Postscript figures (uuencoded
Trajectory versus probability density entropy
We study the problem of entropy increase of the Bernoulli-shift map without
recourse to the concept of trajectory and we discuss whether, and under which
conditions if it does, the distribution density entropy coincides with the
Kolmogorov-Sinai entropy, namely, with the trajectory entropy.Comment: 24 page
Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
Quantum-classical correspondence in conservative chaotic Hamiltonian systems
is examined using a uniform structure measure for quantal and classical phase
space distribution functions. The similarities and differences between quantum
and classical time-evolving distribution functions are exposed by both
analytical and numerical means. The quantum-classical correspondence of
low-order statistical moments is also studied. The results shed considerable
light on quantum-classical correspondence.Comment: 16 pages, 5 figures, to appear in Physical Review
Entropy and Wigner Functions
The properties of an alternative definition of quantum entropy, based on
Wigner functions, are discussed. Such definition emerges naturally from the
Wigner representation of quantum mechanics, and can easily quantify the amount
of entanglement of a quantum state. It is shown that smoothing of the Wigner
function induces an increase in entropy. This fact is used to derive some
simple rules to construct positive definite probability distributions which are
also admissible Wigner functionsComment: 18 page
Fluctuation-dissipation relationship in chaotic dynamics
We consider a general N-degree-of-freedom dissipative system which admits of
chaotic behaviour. Based on a Fokker-Planck description associated with the
dynamics we establish that the drift and the diffusion coefficients can be
related through a set of stochastic parameters which characterize the steady
state of the dynamical system in a way similar to fluctuation-dissipation
relation in non-equilibrium statistical mechanics. The proposed relationship is
verified by numerical experiments on a driven double well system.Comment: Revtex, 23 pages, 2 figure
Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production
Based on the Fokker-Planck and the entropy balance equations we have studied
the relaxation of a dissipative dynamical system driven by external
Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium
constraint in terms of the thermodynamically inspired quantities like entropy
flux and entropy production. The interplay of nonequilibrium constraint,
dissipation and noise reveals some interesting extremal nature in the time
dependence of entropy flux and entropy production.Comment: RevTex, 17 pages, 9 figures. To appear in Phys. Rev.
Towards the Thermodynamics of Localization Processes
We study the entropy time evolution of a quantum mechanical model, which is
frequently used as a prototype for Anderson's localization. Recently Latora and
Baranger [V. Latora, M. Baranger, Phys. Rev.Lett. 82, 520(1999)] found that
there exist three entropy regimes, a transient regime of passage from dynamics
to thermodynamics, a linear in time regime of entropy increase, namely a
thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the
non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J.
Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that
with the adoption of the ``magic'' value q = Q = 1/2 the Kolmogorov regime
becomes more extended and more distinct than with the traditional entropic
index q = 1. We adopt a two-site model to explain these properties by means of
an analytical treatment and we argue that Q =1/2 might be a typical signature
of the occurrence of Anderson's localization.Comment: 13 pages, 8 figures submitted to Phys. Rev.
Environment-induced dynamical chaos
We examine the interplay of nonlinearity of a dynamical system and thermal
fluctuation of its environment in the ``physical limit'' of small damping and
slow diffusion in a semiclassical context and show that the trajectories of
c-number variables exhibit dynamical chaos due to the thermal fluctuations of
the bath.Comment: Revtex, 4 pages and 4 figure
Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps
We calculated, within the Gross-Pitaevskii formalism, the critical number of
atoms for Bose-Einstein condensates with two-body attractive interactions in
cylindrical traps with different frequency ratios. In particular, by using the
trap geometries considered by the JILA group [Phys. Rev. Lett. 86, 4211
(2001)], we show that the theoretical maximum critical numbers are given
approximately by . Our results also show that, by
exchanging the frequencies and , the geometry with
favors the condensation of larger number of particles.
We also simulate the time evolution of the condensate when changing the ground
state from to using a 200ms ramp. A conjecture on higher order
nonlinear effects is also added in our analysis with an experimental proposal
to determine its signal and strength.Comment: (4 pages, 2 figures) To appear in Physical Review
Intrinsic decoherence and classical-quantum correspondence in two coupled delta-kicked rotors
We show that classical-quantum correspondence of center of mass motion in two
coupled delta-kicked rotors can be obtained from intrinsic decoherence of the
system itself which occurs due to the entanglement of the center of mass motion
to the internal degree of freedom without coupling to external environment