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Disappearance of time integrals of exact memory functions in time‐convolution generalized master equations
Author(s) -
Čápek Vladislav
Publication year - 1998
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.2090070305
Subject(s) - master equation , convolution (computer science) , limit (mathematics) , zero (linguistics) , pauli exclusion principle , relaxation (psychology) , exponential function , markov chain , markov process , physics , mathematics , mathematical physics , statistical physics , quantum mechanics , mathematical analysis , computer science , psychology , social psychology , linguistics , philosophy , statistics , machine learning , artificial neural network , quantum
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.