Algebraic conditions for convergence of a quantum Markov semigroup to a steady state

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dc.contributor.authorFagnola, Franco
dc.contributor.authorRebolledo, Rolando
dc.date.accessioned2024-01-10T13:45:43Z
dc.date.available2024-01-10T13:45:43Z
dc.date.issued2008
dc.description.abstractLet T be a uniformly continuous quantum Markov semigroup on B(h) with generator represented in a standard GKSL form L(x) = -1/2 Sigma(l)(L-l*L(l)x - 2L(l)*xL(l) + xL(l)*L-l) + i[H, x] and a faithful normal invariant state rho. In this note we give new algebraic conditions for proving that T converges towards a steady state, possibly different from rho. Indeed, we show that this happens whenever the commutator of {H, L-l, L-l*vertical bar l >= 1} (i.e. its fixed point algebra) coincides with the commutator of {L-l, L-l*, delta(H)(L-l), delta(H)(L-l*), ..., delta(n)(H)(L-l), delta(n)(H)(L-l*)vertical bar l >= 1} (where delta(H)(X) = [H,X]) for some n >= 1. As an application we discuss the convergence to the unique invariant state of a spin chain model.
dc.description.funderGNAMPA-INdAM
dc.description.funderPBCT-ACT13
dc.fechaingreso.objetodigital2024-05-14
dc.format.extent8 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1142/S0219025708003142
dc.identifier.eissn1793-6306
dc.identifier.issn0219-0257
dc.identifier.urihttps://doi.org/10.1142/S0219025708003142
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/79070
dc.identifier.wosidWOS:000258880100009
dc.information.autorucMatemática;Rebolledo R;S/I;99203
dc.issue.numero3
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final474
dc.pagina.inicio467
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD
dc.revistaINFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
dc.rightsacceso restringido
dc.subjectquantum Markov semigroups
dc.subjectapproach to equilibrium
dc.subjectLindblad generator
dc.subjectmultiple commutators
dc.subjectDYNAMICAL SEMIGROUPS
dc.subjectEQUILIBRIUM
dc.subject.ods09 Industry, Innovation and Infrastructure
dc.subject.odspa09 Industria, innovación e infraestructura
dc.titleAlgebraic conditions for convergence of a quantum Markov semigroup to a steady state
dc.typeartículo
dc.volumen11
sipa.codpersvinculados99203
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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