Showing papers on "Quantum evolution published in 1998"

A remark on quantum dynamics

Abstract: Some computations in classical quantum dynamics can be simplified by substituting the Schrodinger Hamil¬ tonian with a different operator. The time evolution can then be obtained by iterating a map. This allows efficiently to determine the Fourier coefficients of the spectral measures of the new Hamiltonian. Many prop¬ erties of the quantum evolution are not affected by the deformation of the Hamiltonian because the spectral measures are only distorted. For example, a numerical computations of the Wiener averages allows to test numerically for the existence of bound states. We illustrate the time discretisation for a tight binding model of an electron in a constant or random magnetic field in the plane. As a theoretical illustration, we relate the return probability for the quantum evolution on a graph to the return probability of the corresponding random walk.

Quantum Recurrent Networks for Simulating Stochastic Processes

Abstract: We introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks. We show that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties finding application in pattern recognition, optimization and simulation. Moreover, decoherence in quantum recurrent networks is less problematic than in conventional quantum network architectures due to the modest phase coherence times needed for network operation.

Quantum 2+1 evolution model

Abstract: A quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system called "the current system". In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical one and it corresponds to known operator-valued R-matrix. The current system is a kind of the linear problem for 2+1 evolution model. A generating function for the integrals of motion for the evolution is derived with a help of the current system. The subject of the paper is rather new, and so the perspectives of further investigations are widely discussed.

Temporal Behavior of Quantum Systems and Quantum Zeno Effect

Abstract: The temporal behavior of an unstable system is analyzed quantum mechanically and compared to the exponential decay law. The general mathematical features of the quantum evolution, yielding a quadratic region at short times and a power law at long times, are briefly reviewed.