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A simple quantum equation for Decoherence and dissipation (through interaction with the environment)

Erasmo Recami·Ruy H. A. Farias
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Abstract

Within the density matrix formalism, it is shown that a simple way to get decoherence is through the introduction of a "quantum" of time (chronon): which implies replacing the differential Liouville--von Neumann equation with a finite-difference version of it. In this way, one is given the possibility of using a rather simple quantum equation to describe the decoherence effects due to dissipation. Namely, the mere introduction (not of a "time-lattice", but simply) of a "chronon" allows us to go on from differential to finite-difference equations; and in particular to write down the quantum-theoretical equations (Schroedinger equation, Liouville--von Neumann equation,...) in three different ways: "retarded", "symmetrical", and "advanced". One of such three formulations --the retarded one-- describes in an elementary way a system which is exchanging (and losing) energy with the environment; and in its density-matrix version, indeed, it can be easily shown that all non-diagonal terms go to zero very rapidly. [A much larger presentation of the theoretical ground on which this paper is based appeared in the e-print quant-ph/9706059, and in the preprint IC/98/74, ICTP; Trieste, 1998].

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Erasmo Recami, Ruy H. A. Farias. 2002-09-01. A simple quantum equation for Decoherence and dissipation (through interaction with the environment). https://doi.org/10.1393/ncb%2Fi2009-10799-1

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