Generalized quantum FokkerPlanck equation for photoinduced nonequilibrium processes with positive definiteness condition
This work provides a detailed derivation of a generalized quantum FokkerPlanck equation (GQFPE) appropriate for photoinduced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and nonMarkovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be inmore »
 Authors:

^{[1]}
 City Univ. (CUNY), NY (United States). Queens College. Dept. of Chemistry and Biochemistry
 Publication Date:
 Grant/Contract Number:
 SC0001393; CHE1362926
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 144; Journal Issue: 21; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 City Univ. (CUNY), NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
 OSTI Identifier:
 1471500
 Alternate Identifier(s):
 OSTI ID: 1255314
Jang, Seogjoo. Generalized quantum FokkerPlanck equation for photoinduced nonequilibrium processes with positive definiteness condition. United States: N. p.,
Web. doi:10.1063/1.4952477.
Jang, Seogjoo. Generalized quantum FokkerPlanck equation for photoinduced nonequilibrium processes with positive definiteness condition. United States. doi:10.1063/1.4952477.
Jang, Seogjoo. 2016.
"Generalized quantum FokkerPlanck equation for photoinduced nonequilibrium processes with positive definiteness condition". United States.
doi:10.1063/1.4952477. https://www.osti.gov/servlets/purl/1471500.
@article{osti_1471500,
title = {Generalized quantum FokkerPlanck equation for photoinduced nonequilibrium processes with positive definiteness condition},
author = {Jang, Seogjoo},
abstractNote = {This work provides a detailed derivation of a generalized quantum FokkerPlanck equation (GQFPE) appropriate for photoinduced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and nonMarkovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. In conclusion, steady state limit of the GQFPE is shown to approach the wellknown expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and nonMarkovian effects of the bath.},
doi = {10.1063/1.4952477},
journal = {Journal of Chemical Physics},
number = 21,
volume = 144,
place = {United States},
year = {2016},
month = {6}
}