This thesis focuses on the study on the two most commonly used quantum dissipation theories, the Bloch-Redfield theory and Fokker-Planck equations and their applications in nonlinear spectroscopies. _{1 2}...[ Read more ]

This thesis focuses on the study on the two most commonly used quantum dissipation theories, the Bloch-Redfield theory and Fokker-Planck equations and their applications in nonlinear spectroscopies.

After the spectrum conjugation to a dissipative mode was introduced, developed is the unified Redfield theory which satisfies the detailed-balance. Base on this unified Redfield theory, a generalized quantum Fokker-Planck equation is developed for both the T₁-energy relaxation and the pure-T₂ dephasing dissipation processes. The resulting dynamical semigroup Fokker-Planck equation preserves the general positivity of the reduced density operator and satisfies the detailed-balance relation up to the second-order moments at any temperatures. (Chapter 1).

In order to understand the molecular dynamics in condensed phase theoretically and experimentally, the application of unified Redfield theory to transient absorption spectroscopies of molecules( Chapter 2) and the implementation of Fokker-Planck equation to transient absorption and fluorescence upconversion spectroscopies( Chapter 3 and Chapter 4) are discussed. Numerical demonstrations are carried out in a model molecule involving two Morse potential surfaces in the presence of the T₁-vibrational relaxation and the pure T₂-dephasing in both nuclear and electronic degrees of freedom. The pump-probe absorption and the time-frequency resolved fluorescence spectra are analyzed in terms of the dissiaptive dynamics.

Chapter 5 presents an interesting application of quantum dissipation theories beyond the spectroscopies. Analyzed is the quantum transport in symmetric two-level systems under the influence of both dissipation and periodic driving.