7 research outputs found
Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
We study the interrelations between the classical (Frobenius-Perron) and the
quantum (Husimi) propagator for phase-space (quasi-)probability densities in a
Hamiltonian system displaying a mix of regular and chaotic behavior. We focus
on common resonances of these operators which we determine by blurring
phase-space resolution. We demonstrate that classical and quantum time
evolution look alike if observed with a resolution much coarser than a Planck
cell and explain how this similarity arises for the propagators as well as
their spectra. The indistinguishability of blurred quantum and classical
evolution implies that classical resonances can conveniently be determined from
quantum mechanics and in turn become effective for decay rates of quantum
correlations.Comment: 10 pages, 3 figure
Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
Resonances of the (Frobenius-Perron) evolution operator P for phase-space
densities have recently attracted considerable attention, in the context of
interrelations between classical and quantum dynamics. We determine these
resonances as well as eigenvalues of P for Hamiltonian systems with a mixed
phase space, by truncating P to finite size in a Hilbert space of phase-space
functions and then diagonalizing. The corresponding eigenfunctions are
localized on unstable manifolds of hyperbolic periodic orbits for resonances
and on islands of regular motion for eigenvalues. Using information drawn from
the eigenfunctions we reproduce the resonances found by diagonalization through
a variant of the cycle expansion of periodic-orbit theory and as rates of
correlation decay.Comment: 18 pages, 7 figure
Semiclassical singularities from bifurcating orbits.
We investigated numerically, for a generic quantum system (a kicked top), how the singular behavior of classical systems at bifurcations is reflected by their quantum counterpart. Good agreement is found with semiclassical predictions