Intensive Lectures part (sponsored by USTC)

1. Feynman path integral and Influence Functional (ppt lecture note) (Mpeg)

The path integral formalism is explained from the beginning using the ppt lecture note "Learn Schrödinger, Dirac & Feynman formalisms in 90 minutes." The Feynman-Vernon influence functional (F-V IF) is derived from the unfactorized initial condition by reducing the bath degrees of freedom. The IF consists of fluctuation and dissipation, and the thermal equilibrium state is established by these two terms satisfying the fluctuation-dissipation theorem, which clearly shows why the Markov approximation does not hold for quantum noise.

2. Quantum Hierarchical Fokker-Planck Equations (ppt lecture note) (Mpeg)

The quantum heretical Fokker-Planck equations (QHFPE) are derived on the basis of the IF formalism. The QHFPE can deal with non-Markovian noise even at very low temperature. This ensures that not only the thermal equilibrium state, but also the dynamical process towards the equilibrium state is correctly described, even when interacting with a non-Markovian and/or non-perturbative heat bath.

3. Hierarchy Equations of Motion (HEOM) for discretized energy states (ppt lecture note) (Mpeg)

The reduced hierarchy equations of motion for system with discrete energy levels are derived using a coherent state representation for the path integrals. The source code, "nonMarkovian2009", will be explained

4. Quantum noise cannot be Markovian (ppt lecture note)  (Mpeg)

 Anomalous features of reduced equations of motion under Markovian assumption are illustrated for the quantum master equation and quantum Fokker-Planck equation in the Lindblad form, Redfield equation, time-convolutionless Redfield equation, derived on the based of (i) the factorized approximation, (ii) the perturbation approximation, (iii) the rotating wave approximation, and (iv) the Markovian assumption.

5. Electron transfer problem, 2D electronic spectroscopies, & Non-Adiabatic Transitions  (ppt lecture note)  (Mpeg) 

We extended QHFPE approach to multi-electrical states, to the calculation of linear and nonlinear spectra for a system described by the multistate potential surfaces interacting with non-perturbative and non-Markovian system-bath interactions. The motion of excitation and ground state wave packets and their coherence involved in the process were observed as the profiles of positive and negative peaks of the 2D electric vibrational spectrum

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