It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of the initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible.In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration.The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems.For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics.It is shown in the paper that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one.The second part of the paper is dedicated to the kinematic description of the chaotic quantummechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration.
a b s t r a c tThe dynamics of an entangled state interacting with a single cavity mode is investigated in the presence of a random parameter. We show that the degree of entanglement decays with time and that the rate of decay is defined by features of a random parameter. Quantum teleportation through a dissipative channel and teleportation fidelity as a function of damping rates have been studied. The sensitivity of the fidelity with respect to the random parameter is discussed. We have evaluated the time interval during which one can perform quantum teleportation and send the information with reasonable fidelity for given values of the correlation length of the random parameter.
The statistics of quantum Poincaré recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincaré recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to a mixed one. Keywords: Diamagnetic Kepler problem; quantum chaos; non-reversible chaos; phase incursion; mixed state formation. PACS Number(s): 05.45.Mt where p, q are a set of classical coordinates and momentum,Ĥ 0 (p, q) is classically an integrable part of Hamiltonian, V (q) is a part of Hamiltonian which leads to the non-integrability of the classical equations of motion when added, λ is a parameter by variation of which the system may be driven in the domain of chaotic dynamics. 79 Mod. Phys. Lett. B 2007.21:79-96. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 02/02/15. For personal use only.
We investigate the generalized Kuhn's model, namely, a chain of nonlinear chaotic oscillators describing a nonlinear gyrotropic medium. It is shown that despite the chaotic behavior of separate oscillators the chain preserves some coherency as a whole. The relation between the chain synchronization and the physical properties of a random mean field is established.
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