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Exact Solutions of the Caldeira-Leggett Master Equation: A Factorization Theorem For Decoherence

S. M. Roy·Anu Venugopalan
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Abstract

Exact solutions of the Caldeira-Leggett Master equation for the reduced density matrix for a free particle and for a harmonic oscillator system coupled to a heat bath of oscillators are obtained for arbitrary initial conditions. The solutions prove that the Fourier transform of the density matrix at time t with respect to (x + x')/2, where x and x' are the initial and final coordinates, factorizes exactly into a part depending linearly on the initial density matrix and a part independent of it. The theorem yields the exact initial state dependence of the density operator at time t and its eventual diagonalization in the energy basis.

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S. M. Roy, Anu Venugopalan. 1999-10-01. Exact Solutions of the Caldeira-Leggett Master Equation: A Factorization Theorem For Decoherence. https://arxiv.org/abs/quant-ph/9910004

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