Mixed quantum-classical dynamics response function approach to spectroscopy

Abstract

Mixed quantum-classical dynamics formulation of Kapral and co-workers has been successfully employed to systems composed of a quantum subsystem coupled to an environment with classical degrees of freedom to study the dynamics of condensed many-body systems. In this formalism the quantum subsystem and the bath dynamics obey the full quantum mechanics, classical mechanics, respectively, whereas the coupling term dynamics is governed by mixed quantum-classical equations. To this end, the linear response function approach in mixed quantum-classical systems is used to derive the optical linear electronic dipole moment time-correlation function of a two-level system coupled to harmonic vibrations in condensed media. The fact that this is an exactly solvable model using full quantum mechanics allows us to test the applicability of the presented approach. An alternative approach to the aforementioned method is also developed as a second method to further test the applicability of the linear response function approach in mixed quantum-classical systems, and to confirm the correctness of the end result when using mixed quantum-classical dynamics formulation of Kapral and co-workers. Both approaches are found to yield identical results. These results are compared to those of the full quantum results in the high temperature limit. Model application of electronic absorption spectra is presented. Optical nonlinear response functions are also obtained in mixed quantum-classical systems with only linear electron–phonon coupling.