Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution that is used to study the time evolution of the reduced density operator. It is derived in a closed form, in the one-particle sector of the model. The irreversible behavior of the Brownian particle is described by a reduced density matrix.

Jan 1, 200015 citations

arXiv:quant-ph/0005041 · Physica A Statistical Mechanics and its Applications

Minimal irreversible quantum mechanics. The decay of unstable states

Diego G. Arbó, Mario A. Castagnino, Fabián H. Gaioli, Sergio Iguri

Published Mar 1, 2000• 11 citations

arXiv HTML PDF

DOI: 10.1016/s0378-4371(99)00480-x

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Minimal irreversible quantum mechanics. The decay of unstable states

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t \to \infty .

These ''Gamov vectors'' have zero norm, in such a way that the norm and the energy of the physical states remain constant. The evolution operator has no inverse, showing that we are really dealing with a time-asymmetric theory. Using Friedrichs model reasonable physical results are obtained, e. g. : the remaining of an unstable decaying state reappears, in the continuous spectrum of the model, with its primitive energy.