Weak-Coupling Limit. II On the Quantum Fokker-Planck Equation TeX Export

@article{citeulike:4623283, abstract = {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.}, archivePrefix = {arXiv}, author = {Taj, David}, citeulike-article-id = {4623283}, citeulike-linkout-0 = {http://arxiv.org/abs/0905.1019}, citeulike-linkout-1 = {http://arxiv.org/pdf/0905.1019}, day = {7}, eprint = {0905.1019}, keywords = {algebras, open, systems}, month = {May}, posted-at = {2009-05-24 20:23:22}, priority = {2}, title = {Weak-Coupling Limit. II On the Quantum Fokker-Planck Equation}, url = {http://arxiv.org/abs/0905.1019}, year = {2009} }

TY - JOUR ID - citeulike:4623283 L3 - citeulike-article-id:4623283 N2 - 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. TI - Weak-Coupling Limit. II On the Quantum Fokker-Planck Equation KW - algebras KW - open KW - systems AU - Taj, David PY - 2009/May/07/ UR - http://arxiv.org/abs/0905.1019 ER -