Eliade Stefanescu - OPEN QUANTUM SYSTEMS

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  Publication Details (including relevant citation   information):

  International Journal of Modern Physics E 3 (1994) 635-714.


  The damping of the harmonic oscillator is studied in the   framework of  the Lindblad theory for open quantum systems.   A generalization of the  fundamental constraints on quantum   mechanical diffusion coefficients  which appear in the   master equation for the damped quantum oscillator is    presented; the Schrödinger, Heisenberg and   Weyl-Wigner-Moyal  representations of the Lindblad equation   are given explicitly. On the  basis of these representations   it is shown that various master equations  for the damped   quantum oscillator used in the literature are particular    cases of the Lindblad equation and that not all of these   equations are  satisfying the constraints on quantum   mechanical diffusion coefficients.  Analytical expressions   for the first two moments of coordinate and  momentum are   obtained by using the characteristic function of the    Lindblad master equation. The master equation is transformed   into  Fokker-Planck equations for quasiprobability   distributions and a  comparative study is made for the   Glauber P representation, the  antinormal ordering Q   representation, and the Wigner W representation.  The   density matrix is represented via a generating function, which   is  obtained by solving a timedependent linear partial   differential equation  derived from the master equation.   Illustrative examples for specific  initial conditions of   the density matrix are provided. The solution of  the master   equation in the Weyl-Wigner-Moyal representation is of    Gaussian type if the initial form of the Wigner function is taken   to be a  Gaussian corresponding (for example) to a coherent   wavefunction. The  damped harmonic oscillator is applied for   the description of the charge  equilibration mode observed   in deep inelastic reactions. For a system  consisting of two   harmonic oscillators the time dependence of  expectation   values, Wigner function and Weyl operator, are obtained and    discussed. In addition models for the damping of the angular   momentum  are studied. Using this theory to the quantum   tunneling through the  nuclear barrier, besides Gamow’s   transitions with energy conservation,  additional   transitions with energy loss are found. The tunneling    spectrum is obtained as a function of the barrier   characteristics. When  this theory is used to the resonant   atom-field interaction, new optical  equations describing   the coupling through the environment of the atomic    observables are obtained. With these equations, some   characteristics of  the laser radiation absorption spectrum   and optical bistability are  described.

  Address (URL): http://www.worldscinet.com/ijmpe/03/0302/S0218301394000164.html