15 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
Coarse Grained Liouville Dynamics of piecewise linear discontinuous maps
We compute the spectrum of the classical and quantum mechanical
coarse-grained propagators for a piecewise linear discontinuous map. We analyze
the quantum - classical correspondence and the evolution of the spectrum with
increasing resolution. Our results are compared to the ones obtained for a
mixed system.Comment: 11 pages, 8 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
Dissipation time and decay of correlations
We consider the effect of noise on the dynamics generated by
volume-preserving maps on a d-dimensional torus. The quantity we use to measure
the irreversibility of the dynamics is the dissipation time. We focus on the
asymptotic behaviour of this time in the limit of small noise. We derive
universal lower and upper bounds for the dissipation time in terms of various
properties of the map and its associated propagators: spectral properties,
local expansivity, and global mixing properties. We show that the dissipation
is slow for a general class of non-weakly-mixing maps; on the opposite, it is
fast for a large class of exponentially mixing systems which include uniformly
expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit
Propagating wave correlations in complex systems
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures
Spectral properties of noisy classical and quantum propagators
We study classical and quantum maps on the torus phase space, in the presence
of noise. We focus on the spectral properties of the noisy evolution operator,
and prove that for any amount of noise, the quantum spectrum converges to the
classical one in the semiclassical limit. The small-noise behaviour of the
classical spectrum highly depends on the dynamics generated by the map. For a
chaotic dynamics, the outer spectrum consists in isolated eigenvalues
(``resonances'') inside the unit circle, leading to an exponential damping of
correlations. On the opposite, in the case of a regular map, part of the
spectrum accumulates along a one-dimensional ``string'' connecting the origin
with unity, yielding a diffusive behaviour. We finally study the
non-commutativity between the semiclassical and small-noise limits, and
illustrate this phenomenon by computing (analytically and numerically) the
classical and quantum spectra for some maps.Comment: 35 pages, 6 .eps figures, to be published in Nonlinearity. I added
some references and comment
District heating and the Integration of renewable energy sources: A chance for rural areas
In various countries small-scale district heating networks in rural areas have been build or taken into advanced stage of planning. In some cases heat is generated from renewable energy sources or in combined heat and power plants. Conducted interviews have returned that the biomass heating technology is mature and reliable and the operation of small district heating networks is generally well tested