Dissipation and decoherence (for example, the effects of noise in quantum computations), interaction with a thermostat (or in general with a physical vacuum), measurement, and many other complicated problems in open quantum systems, are a consequence of the interaction of quantum systems with the environment. These problems are described mathematically in terms of complex probabilistic processes (CPP). In treating the environment as a Markovian process, we derive a Langevin-Schrödinger type stochastic differential equation (SDE) for describing the quantum system's interaction with the environment. For the 1D randomly quantum harmonic oscillator (QHO) model, L-Sh SDE is a solution ??in the form of?? orthogonal CPP. On the basis of orthogonal CPP, the stochastic density matrix (SDM) method is developed and in its framework, the relaxation processes in the uncountable dimension closed system of the “QHO + environment” are investigated. Using the SDM method, thermodynamical potentials such as nonequilibrium entropy and the energy of the ground state are constructed. The dispersions for different operators are calculated. In particular, the expression for uncertain relations depending on the parameters of interaction with the environment is obtained. The Weyl transformation for stochastic operators is specified, and the Ground state Winger function is developed in detail.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com