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

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

2002-06-18

arxiv.org/abs/quant-ph/0206117v3

Nuovo Cimento B147 (2009) 765-776

Physics

Quantum Physics

plain LaTeX file (15 pages), plus 1 figure. Replaced with improvements

Scientific paper

10.1393/ncb/i2009-10799-1

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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