Non-Markovian theory of open systems in classical limit

Abstract

A fully classical limit of the recently published quantum-classical approximation [A. A. Neufeld, J. Chem. Phys. 119, 2488 (2003)] is obtained and analyzed. The resulting kinetic equations are capable of describing the evolution of an open system on the entire time axis, including the short-time non-Markovian stage, and are valid beyond linear response regime. We have shown, that proceeding to the classical mechanics limit we restrict the class of allowed correlations between an open system and a canonical bath, so that the initial conditions and the relaxation operator has to be appropriately modified (projected). Disregard of the projection may lead to unphysical behavior, since mechanism of the decay of some correlations is essentially of quantum-mechanical nature, and is not correctly described by classical mechanics. The projection (quantum correction to the kinetics) is particularly important for the non-Markovian regime of relaxation towards canonical equilibrium. The conformity of the developed method to the conventional approaches is demonstrated using a model of Brownian motion (heavy particle in the bath of light ones), for which the obtained non-Markovian equations are reduced to the standard Fokker-Planck equation in phase space.

Critical appraisal of the fewest switches algorithm for surface hopping

“…Moreover, there is no generally accepted definition for a mixed quantum/classical system ͑as observed by Caro and Salcedo, 15 this is because no such systems exist in nature͒ and then, a very large number of quantum/classical schemes have been developed, ranging from methods based on independent trajectories [16][17][18][19] to more complicated approaches in which at least some aspects of the quantum nature of the nuclear motion are retained: full multiple spawning, 20 quantum/classical Liouville dynamics, [20][21][22][23][24][25][26] Bohmian trajectories, 27 path integrals, 28 and many others. [29][30][31][32][33][34] However, the TSH method in its most popular implementation, i.e., Tully's "fewest switches" approach 7 ͑TFS͒, is still a good compromise between computational efficiency, conceptual simplicity, and accuracy of results, 17 especially for medium-sized and large molecular systems. 35 In this algorithm the electronic density matrix is propagated coherently along the trajectory and the transition probability is evaluated taking into account the variation in time of the diagonal density matrix elements.…”

Statistical theory of nonadiabatic transitions

“…The latter becomes dominant at ͉Ŵ nk ͑q͉͒ b / បտ1, see also Ref. 60, and the true adiabaticity is reached in this limit even at diffusive motion. On the other hand, the small parameter ͑5͒ of the theory does not coincide with the familiar Massey parameter, which is used to distinguish between adiabatic and nonadiabatic regimes in the absence of a thermal bath.…”

Theory of solvent influence on reaction dynamics

“…Second, the decay of some correlations between the reacting system and the canonical bath is essentially of quantummechanical nature, and is not correctly described by classical mechanics, so that the nonequilibrium energy flow between the subsystems has both "classical" and "quantum" components, see Ref. 44 for more details.…”

“…The latter becomes dominant if the condition ͑8͒ is not fulfilled ͑see Ref. 44 for more details͒ and, therefore, the classical mechanics treatment of the bath seems to be problematic in this limit.…”