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Decoherence and Dissipation in Quantum Two-State Systems

M. Grigorescu
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Abstract

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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M. Grigorescu. 1997-09-16. Decoherence and Dissipation in Quantum Two-State Systems. https://doi.org/10.1016/s0378-4371(98)00076-4

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