Chaotic density matrix in the classical limit

Gaspar Gonzalez, Angel Ricardo Plastino, Andrés M. Kowaslki

Alessandro Farini, Stefano Boccaletti, F. T. Arecchi

We introduce a characteristic time of a classical chaotic dynamics, represented by the coherence time of the local maximum expansion direction. For a quantum system whose classical limit follows the above chaotic dynamics, the ratio between this time and the decorrelation time (of the order of the reciprocal of the maximum Liapunov exponent) rules the ratio between nonclassical (Moyal) and classical (Liouville) terms in the evolution of the density matrix. We show that such a ratio does not provide a complete criterion for quantum-classical correspondence.

M. Fannes

Pablo Bianucci, Juan Pablo Paz, Marcos Saraceno

We study the behavior of an open quantum system, with an N-dimensional space of states, whose density matrix evolves according to a nonunitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's map and Harper's map are the two examples we consider). A nonunitary step where the evolution operator for the density matrix mimics the effect of diffusion in the semiclassical (large N) limit. The process of decoherence and the transition from quantum to classical behavior are analyzed in detail by means of numerical and analytic tools. The existence of a regime where the entropy grows with a rate that is independent of the strength of the diffusion coefficient is demonstrated. The nature of the processes that determine the production of entropy is analyzed.

Rui-hua Xie, Ruibao Tao, Gong-ou Xu

Joshua Wilkie, Paul W. Brumer

We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to approach their classical analogs in the h\ensuremath{\rightarrow}0 limit. Correspondence is shown to occur via the elimination of essential singularities. In addition, applications to matrix elements of observables in chaotic systems are discussed.