TY - JOUR
T1 - Asymptotic stochastic transformations for nonlinear quantum dynamical systems
AU - Gough, John
N1 - Funding Information:
This work was supported by the Irish Higher Education Authority’s EU Presidency Research Fellowship Program and the author would like to thank Professor D. Heffernan (Maynooth) for many stimulatingd iscussionsw hile writing this paper. The author also acknowledgesm any valuable commentsm ade by the referee which have lead to an improvementt o the original version.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1999/12
Y1 - 1999/12
N2 - The Ito and Stratonovich approaches are carried over to quantum stochastic systems. Here the white noise representation is shown to be the most appropriate as here the two approaches appear as Wick and Weyl orderings, respectively. This introduces for the first time the Stratonovich form for SDEs driven by Poisson processes or quantum SDEs including the conservation process. The relation of the nonlinear Heisenberg ODEs to asymptotic quantum SDEs is established extending previous work on linear (Schrödinger) equations. This is shown to generalize the classical integral transformations between the various forms of stochastic calculi and to extend the Khasminskii theorem to the quantum setting.
AB - The Ito and Stratonovich approaches are carried over to quantum stochastic systems. Here the white noise representation is shown to be the most appropriate as here the two approaches appear as Wick and Weyl orderings, respectively. This introduces for the first time the Stratonovich form for SDEs driven by Poisson processes or quantum SDEs including the conservation process. The relation of the nonlinear Heisenberg ODEs to asymptotic quantum SDEs is established extending previous work on linear (Schrödinger) equations. This is shown to generalize the classical integral transformations between the various forms of stochastic calculi and to extend the Khasminskii theorem to the quantum setting.
UR - http://www.scopus.com/inward/record.url?scp=0033473630&partnerID=8YFLogxK
U2 - 10.1016/s0034-4877(00)87242-0
DO - 10.1016/s0034-4877(00)87242-0
M3 - Article
AN - SCOPUS:0033473630
SN - 0034-4877
VL - 44
SP - 313
EP - 338
JO - Reports on Mathematical Physics
JF - Reports on Mathematical Physics
IS - 3
ER -