247 research outputs found
Exactly solvable model of quantum diffusion
We study the transport property of diffusion in a finite translationally
invariant quantum subsystem described by a tight-binding Hamiltonian with a
single energy band and interacting with its environment by a coupling in terms
of correlation functions which are delta-correlated in space and time. For weak
coupling, the time evolution of the subsystem density matrix is ruled by a
quantum master equation of Lindblad type. Thanks to the invariance under
spatial translations, we can apply the Bloch theorem to the subsystem density
matrix and exactly diagonalize the time evolution superoperator to obtain the
complete spectrum of its eigenvalues, which fully describe the relaxation to
equilibrium. Above a critical coupling which is inversely proportional to the
size of the subsystem, the spectrum at given wavenumber contains an isolated
eigenvalue describing diffusion. The other eigenvalues rule the decay of the
populations and quantum coherences with decay rates which are proportional to
the intensity of the environmental noise. On the other hand, an analytical
expression is obtained for the dispersion relation of diffusion. The diffusion
coefficient is proportional to the square of the width of the energy band and
inversely proportional to the intensity of the environmental noise because
diffusion results from the perturbation of quantum tunneling by the
environmental fluctuations in this model. Diffusion disappears below the
critical coupling.Comment: Submitted to J. Stat. Phy
Semiclassical theory of the emission properties of wave-chaotic resonant cavities
We develop a perturbation theory for the lifetime and emission intensity for
isolated resonances in asymmetric resonant cavities. The inverse lifetime
and the emission intensity in the open system are
expressed in terms of matrix elements of operators evaluated with eigenmodes of
the closed resonator. These matrix elements are calculated in a semiclassical
approximation which allows us to represent and as sums
over the contributions of rays which escape the resonator by refraction.Comment: 4 pages, 2 color figure
Microwave study of quantum n-disk scattering
We describe a wave-mechanical implementation of classically chaotic n-disk
scattering based on thin 2-D microwave cavities. Two, three, and four-disk
scattering are investigated in detail. The experiments, which are able to probe
the stationary Green's function of the system, yield both frequencies and
widths of the low-lying quantum resonances. The observed spectra are found to
be in good agreement with calculations based on semiclassical periodic orbit
theory. Wave-vector autocorrelation functions are analyzed for various
scattering geometries, the small wave-vector behavior allowing one to extract
the escape rate from the quantum repeller. Quantitative agreement is found with
the value predicted from classical scattering theory. For intermediate
energies, non-universal oscillations are detected in the autocorrelation
function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include
Fluctuation theorem for currents and Schnakenberg network theory
A fluctuation theorem is proved for the macroscopic currents of a system in a
nonequilibrium steady state, by using Schnakenberg network theory. The theorem
can be applied, in particular, in reaction systems where the affinities or
thermodynamic forces are defined globally in terms of the cycles of the graph
associated with the stochastic process describing the time evolution.Comment: new version : 16 pages, 1 figure, to be published in Journal of
Statistical Physic
Classical transients and the support of open quantum maps
The basic ingredients in a semiclassical theory are the classical invariant
objects serving as a support for the quantization. Recent studies, mainly
obtained on quantum maps, have led to the commonly accepted belief that it is
the classical repeller -- the set of non escaping orbits in the future and past
evolution -- the object that suitably plays this role in open scattering
systems. In this paper we present numerical evidence warning that this may not
always be the case. For this purpose we study recently introduced families of
tribaker maps [L. Ermann, G.G. Carlo, J.M. Pedrosa, and M. Saraceno, Phys. Rev.
E {\bf 85}, 066204 (2012)], which share the same asymptotic properties but
differ in their short time behavior. We have found that although the eigenvalue
distribution of the evolution operator of these maps follows the fractal Weyl
law prediction, the theory of short periodic orbits for open maps fails to
describe the resonance eigenfunctions of some of them. This is a strong
indication that new elements must be included in the semiclassical description
of open quantum systems.Comment: 7 pages, 9 figure
Posterior probability and fluctuation theorem in stochastic processes
A generalization of fluctuation theorems in stochastic processes is proposed.
The new theorem is written in terms of posterior probabilities, which are
introduced via the Bayes theorem. In usual fluctuation theorems, a forward path
and its time reversal play an important role, so that a microscopically
reversible condition is essential. In contrast, the microscopically reversible
condition is not necessary in the new theorem. It is shown that the new theorem
adequately recovers various theorems and relations previously known, such as
the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the
Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page
Dissipative chaotic scattering
We show that weak dissipation, typical in realistic situations, can have a
metamorphic consequence on nonhyperbolic chaotic scattering in the sense that
the physically important particle-decay law is altered, no matter how small the
amount of dissipation. As a result, the previous conclusion about the unity of
the fractal dimension of the set of singularities in scattering functions, a
major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte
Efficiency of Free Energy Transduction in Autonomous Systems
We consider the thermodynamics of chemical coupling from the viewpoint of
free energy transduction efficiency. In contrast to an external
parameter-driven stochastic energetics setup, the dynamic change of the
equilibrium distribution induced by chemical coupling, adopted, for example, in
biological systems, is inevitably an autonomous process. We found that the
efficiency is bounded by the ratio between the non-symmetric and the
symmetrized Kullback-Leibler distance, which is significantly lower than unity.
Consequences of this low efficiency are demonstrated in the simple two-state
case, which serves as an important minimal model for studying the energetics of
biomolecules.Comment: 4 pages, 4 figure
Spectral behavior of contractive noise
We study the behavior of the spectra corresponding to quantum systems
subjected to a contractive noise, i.e. the environment reduces the accessible
phase space of the system, but the total probability is conserved. We find that
the number of long lived resonances grows as a power law in but
surprisingly there is no relationship between the exponent of this power law
and the fractal dimension of the corresponding classical attractor. This is in
disagreement with the predictions of the fractal Weyl law which has been
established for open systems where the probability is lost under the effect of
a projective noise.Comment: 5 pages, 8 figure
Predictability in the large: an extension of the concept of Lyapunov exponent
We investigate the predictability problem in dynamical systems with many
degrees of freedom and a wide spectrum of temporal scales. In particular, we
study the case of turbulence at high Reynolds numbers by introducing a
finite-size Lyapunov exponent which measures the growth rate of finite-size
perturbations. For sufficiently small perturbations this quantity coincides
with the usual Lyapunov exponent. When the perturbation is still small compared
to large-scale fluctuations, but large compared to fluctuations at the smallest
dynamically active scales, the finite-size Lyapunov exponent is inversely
proportional to the square of the perturbation size. Our results are supported
by numerical experiments on shell models. We find that intermittency
corrections do not change the scaling law of predictability. We also discuss
the relation between finite-size Lyapunov exponent and information entropy.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
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