1999/10/01 by S. M. Roy, Roy, S. M., Anu Venugopalan +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9910004
8 pages, latex
arxiv created 1999/10/01 · arxiv updated 2009/12/01
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.