Quantum-classical correspondence in response theory

Abstract

In this thesis, theoretical analysis of correspondence between classical and quantum dynamics is studied in the context of response theory. Thesis discusses the mathematical origin of time-divergence of classical response functions and explains the failure of classical dynamic perturbation theory. The method of phase space quantization and the method of semiclassical corrections are introduced to converge semiclassical expansion of quantum response function. The analysis of classical limit of quantum response functions in the Weyl-Wigner representation reveals the source of time-divergence of classical response functions and shows the non-commutativity of the limits of long time and small Planck constant. The classical response function is obtained as the leading term of the h-expansion of the Weyl-Wigner phase space representation and increases without bound at long times as a result of ignoring divergent higher order contributions. Systematical inclusion of higher order contributions improves the accuracy of the h expansion at finite times. The time interval for the quantum-classical correspondence is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity. The effects of dissipation on the correspondence between classical and quantum response functions are studied. The quantum-classical correspondence is shown to improve if coupling to the environment is introduced. In the last part of thesis the effect of quantum chaos on photon echo-signal of two-electronic state molecular systems is studied. The temporal photon echo signal is shown to reveal key information about the nuclear dynamics in the excited electronic state surface.

(cont.) The suppression of echo signals is demonstrated as a signature of level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state.