Decoherence and Dissipation in Quantum Two-State Systems

Details Decoherence and Dissipation in Quantum Two-State Systems Decoherence and Dissipation in Quantum Two-State Systems

1997-09-16

arxiv.org/abs/quant-ph/9709033v2

Physica A256 (1998) 149-162

Physics

Quantum Physics

17 pages, LaTex, 3 postscript figures; replaced to correct typo in Eq. (5)

Scientific paper

The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of freedom are simulated by classical harmonic oscillators, while the dynamical variables of the quantum system are two non-hermitian "square root operators" defined by a Gauss-like decomposition of the density operator. The rate of the noise-induced transitions is expressed as a function of the environmental spectral density, and is discussed for the case of the white noise and blackbody radiation. The result is compared with the rate determined by a quantum environment, calculated by partial tracing in the whole Hilbert space. The time-dependence of the von Neumann entropy and of the dissipated energy is obtained numerically for a system of two quantum states. These are the ground and first excited state of the center of mass vibrations for an ion confined in a harmonic trap.

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