TY - JOUR

T1 - Stochastic Canonical Flows

AU - Gough, John

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2000/9

Y1 - 2000/9

N2 - There has been some opposition to the use of Markov processes in quantum mechanics based upon the fact that no quantum mechanical regression principle can be applied. It is argued here however that one may just as well conclude that there is no classical mechanical regression principal either. The dissipative component of a canonical stochastic flow is of the form of a double Poisson bracket 1/2{{·, Fα}Fα} while the vector component of the noise is the Hamiltonian vector field {·, Fα}; thus the dissipative term is smoother than the noise coefficient. In contrast, the classical Langevin theory is based upon the Ornstein-Uhlenbeck process which has linear drift and constant noise coefficient. Preservation of the canonical structure is at odds with the approximation procedure by Ornstein-Uhlenbeck processes and this is the case in both classical and quantum situations.

AB - There has been some opposition to the use of Markov processes in quantum mechanics based upon the fact that no quantum mechanical regression principle can be applied. It is argued here however that one may just as well conclude that there is no classical mechanical regression principal either. The dissipative component of a canonical stochastic flow is of the form of a double Poisson bracket 1/2{{·, Fα}Fα} while the vector component of the noise is the Hamiltonian vector field {·, Fα}; thus the dissipative term is smoother than the noise coefficient. In contrast, the classical Langevin theory is based upon the Ornstein-Uhlenbeck process which has linear drift and constant noise coefficient. Preservation of the canonical structure is at odds with the approximation procedure by Ornstein-Uhlenbeck processes and this is the case in both classical and quantum situations.

UR - http://www.scopus.com/inward/record.url?scp=0346355719&partnerID=8YFLogxK

U2 - 10.1023/a:1009603716364

DO - 10.1023/a:1009603716364

M3 - Article

AN - SCOPUS:0346355719

SN - 1230-1612

VL - 7

SP - 277

EP - 296

JO - Open Systems and Information Dynamics

JF - Open Systems and Information Dynamics

IS - 3

ER -