Disappearance of time integrals of exact memory functions in time-convolution generalized master equations

Memory functions in time‐convolution Generalized Master Equations (GME) for probabilities of finding a general system (interacting by a general coupling with a true thermodynamic bath) in individual states are considered without resorting to any approximation. After taking the thermodynamic bath lim...

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Bibliographic Details
Published inAnnalen der Physik Vol. 510; no. 3; pp. 201 - 213
Main Author Čápek, Vladislav
Format Journal Article
LanguageEnglish
Published Leipzig WILEY-VCH Verlag 1998
WILEY‐VCH Verlag
Subjects
Kinetics
Master equation
Memory integral
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Summary:Memory functions in time‐convolution Generalized Master Equations (GME) for probabilities of finding a general system (interacting by a general coupling with a true thermodynamic bath) in individual states are considered without resorting to any approximation. After taking the thermodynamic bath limit, time integrals from zero to infinite times of the memories are considered. It is argued that these integrals entering, e.g., the usual naive Markov approximation converting GME the Pauli master (PME) equations are exactly zero. This implies long‐time tails of memories (unobtainable by perturbational expansions) and slower‐than‐exponential long‐time asymptotics of relaxation.
Bibliography:ArticleID:ANDP19985100305
istex:2B5315701AF2840EE74469BB1BCFE00572D639D5
ark:/67375/WNG-7S4S73BT-G
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.19985100305