2009/05/07 by Taj, David
#FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.0905.1019
In a recent work we have found a contraction semigroup able to correctly approximate a projected and perturbed one-parameter group of isometries in a generic Banach space, in the limit of weak-coupling. Here we study its generator by specializing to W^*-algebras: after defining a Physical Subsystem in terms of a completely positive projecting conditional expectation, we find that it generates a Quantum Dynamical Semigroup. As a consequence of uniqueness and strong generality (well defined dynamics, irrespective of the Physical Subsystem spectral properties or dimensions), its generator deserves to be referred as "the" Quantum Fokker-Planck Equation. We then provide important examples of the limit dynamics, one of which constitutes a new Quantum generalization of the celebrated Fermi Golden Rule.