9 research outputs found
Different Traces of Quantum Systems Having the Same Classical Limit
Many quantum systems may have the same classical limit. We argue that in the
classical limit their traces do not necessarily converge one to another. The
trace formula allows to express quantum traces by means of classical quantities
as sums over periodic orbits of the classical system. To explain the lack of
convergence of the traces we need the quantum corrections to the classical
actions of periodic orbits. The four versions of the quantum baker map on the
sphere serve as an illustration of this problem.Comment: LaTeX 4 pages, 2 figures included, final published versio
Irreversible Quantum Baker Map
We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.Comment: 4 pages, 3 figures include
Experimental simulation of quantum graphs by microwave networks
We present the results of experimental and theoretical study of irregular,
tetrahedral microwave networks consisting of coaxial cables (annular
waveguides) connected by T-joints. The spectra of the networks were measured in
the frequency range 0.0001-16 GHz in order to obtain their statistical
properties such as the integrated nearest neighbor spacing distribution and the
spectral rigidity. The comparison of our experimental and theoretical results
shows that microwave networks can simulate quantum graphs with time reversal
symmetry. In particular, we use the spectra of the microwave networks to study
the periodic orbits of the simulated quantum graphs. We also present
experimental study of directional microwave networks consisting of coaxial
cables and Faraday isolators for which the time reversal symmetry is broken. In
this case our experimental results indicate that spectral statistics of
directional microwave networks deviate from predictions of Gaussian orthogonal
ensembles (GOE) in random matrix theory approaching, especially for small
eigenfrequency spacing s, results for Gaussian unitary ensembles (GUE).
Experimental results are supported by the theoretical analysis of directional
graphs.Comment: 16 pages, 7 figures, to be published in Phys. Rev.
Dynamical entropy for systems with stochastic perturbation
Dynamics of deterministic systems perturbed by random additive noise is
characterized quantitatively. Since for such systems the KS-entropy diverges we
analyse the difference between the total entropy of a noisy system and the
entropy of the noise itself. We show that this quantity is non negative and in
the weak noise limit is conjectured to tend to the KS-entropy of the
deterministic system. In particular, we consider one-dimensional systems with
noise described by a finite-dimensional kernel, for which the Frobenius-Perron
operator can be represented by a finite matrix.Comment: REVTeX 18 pages, 9 figures Revised section II, some minor
improvements and correction