The Quasiclassical Statistical Description of Quantum Dynamical Systems and Quantum Chaos

B. Kaulakys

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigenvalues of chaotic systems, while the classical chaos may be derived from quantum equations only introducing the decoherence process due to interaction with system's environment or intermediate frequent measurement. We may conclude that continuously observable quasiclassical system evolves essentially classically-like.

N. G. van Kampen

Klaus Richter

R. Steib, J. L. Schoendorff, H. J. Korsch +1 more

Statistical and dynamical properties of a quasiparticle coupled to polarization vibrations in a dimer model are investigated using a full quantum-mechanical approach. The propagation of the system is described in terms of spin-boson coherent states and compared to various quasiclassical descriptions of the system. The spectrum of the energy eigenvalues and the level spacing distributions of the system are calculated and turn out to be almost regular, especially in the strong coupling limit. It is demonstrated that the usual quasiclassical approach to this problem is not quite satisfactory. This is because the quantum fluctuations in the spin variable give rise to entangled states and correlations which hence should be included in a quasiclassical description. We show that a limited but satisfactory quasiclassical approximation may be given using a suitable integrable reference Hamiltonian.

Hiroshi Fujisaki

A nonadiabatic transition system which exhibits "quantum chaotic" behavior [H. Fujisaki and K. Takatsuka, Phys. Rev. E 63, 066221 (2001)] is investigated from quasiclassical aspects. Since such a system does not have a naive classical limit, we take the mapping approach [Stock and Thoss, Phys. Rev. Lett. 78, 578 (1997)] to represent the quasiclassical dynamics of the system. We numerically show that there is a sound correspondence between the quantum chaos and classical chaos for the system.

Sebastian Müller