Seminar part

1. Hierarchical Fokker-Planck Equation for quantum transport problem: dissipative tunneling [@ Fudan University] (ppt lecture note) (Mpeg)

The effects of fluctuations and dissipation in transport processes are studied using the quantum hierarchical Fokker-Planck equations (QHFPE). For a ratchet problem, we find that when the tunneling effect is dominant, the ratchet potential is effectively lower and the ratchet current decreases. For a resonant tunneling problem, we rigorously evaluate the tunneling current for different bias voltages. We find that in the negative differential resistance regime, hysteresis and plateau-like behavior are observed due to self-current oscillation.

　

2. Hierarchical Fokker-Planck Equations for rotationally invariant system-bath model with gauge fields [@Hangzhou Normal Univ. and Hangzhou Dianzu Univ.] (ppt lecture note) (Mpeg)

 We consider a rotationally invariant system-bath (RISB) model in three-dimensional space that is described by a rotor independently coupled to three harmonic-oscillator baths through functions of the Euler angles. The Caldeira-Leggett (CL) model have been used to describe such systems, but they do not possess rotational symmetry, they cannot describe the discretized rotational bands in absorption and emission spectra that have been found experimentally. Due to a difference in the energy discretization of the total Hamiltonian, the dynamics described by the RISB model differ significantly from those described by the CL model, while both models reduce to the Langevin equation for a rotator in the classical limit. To demonstrate this point, we compute the rotational absorption spectrum defined by the linear response function of a rotator dipole.  As an extension of the RISB, we also derive gauge-invariant QHFPE and study the effect of gauge fields in Aharonov-Bohm rings.

3. Modeling, Calculating, Analyzing Multidimensional Vibrational Spectroscopies: HEOM Approach  [@ Westlake University] (ppt lecture note) (Mpeg)

Spectral line shapes in the condensed phase contain information about various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. In this talk I will explore and describe the role of different physical phenomena that arise from the peculiarities of dissipative dynamics in multidimensional spectra. The methodology will be illustrated by calculating multidimensional signals for water in 2D infrared, 2D THz-Raman, and 2D IR-Raman spectra obtained from an equilibrium-non-equilibrium hybrid MD simulation algorithm. These signals are analyzed in terms of anharmonicity and nonlinear polarizability of vibrational modes using a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions from the quantum hierarchical Fokker-Planck equations (QHFPE) approach for non-Markovian noise. All characteristic 2D profiles of the signals obtained from MD are reproduced by the LL+SL BO model, indicating that this model captures the essential features of the inter- and intra-molecular motion.

4. Non-equilibrium quantum thermodynamics described as intensive & extensive variables  [@ Zhejiang University] (ppt lecture note) (Mpeg)

We formulate a thermodynamic theory applicable to both classical and quantum systems on the basis of the HEOM formalism. These systems are depicted as thermodynamic system–bath model consists of multiple heat baths at time-dependent inverse temperatures \beta(t) capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the dimensionless (DL) minimum work principles for intensive work, \tilde{W}^{int| (t)\ge ∆\Xi(t)=\beta^{qst}(t)∆F^{qst}(t) and for extensive work \tilde{W}^{ext}(t)\ge \Phi^{qst}(t)=\beta^{qst}(t)∆G^{qst}(t), where \Xi(t) and \Phi(t) are the Planck and Massieu potentials derived from quasi-static (qst) changes of intensive and extensive external perturbations and temperature. These inequalities are the generalization of the Kelvin-Planck statement of the second law of thermodynamics. Through use of the above we evaluate the Massieu–Planck potentials as entropic potentials and the Helmholtz–Gibbs potentials as free energy. On the basis of these results, we further develop non-equilibrium thermodynamic potentials expressed in terms of non-equilibrium extensive and intensive variables in time derivative form.

5. Molecular dynamics approaches to simulating multidimensional vibrational spectroscopies  [@ Hangzhou Dianzu Univ.] (ppt lecture note) (Mpeg)

In this lecture, it will be explained how multidimensional vibrational spectroscopy is calculated from a molecular dynamics approach. I will show how linear absorption spectra and Raman spectra are defined. Then explain the calculation methods for 2D Raman, 2D IR, 2D Raman-Terahertz, and 2D Raman-IR spectroscopy performed on them or a combination of them.

6. Simulating Multidimensional Electronic & Electronic-Vibrational Spectroscopies  [@ Ningbo Univ.] (ppt lecture note) (Mpeg)

The simulation of coupled electron-nucleus dynamics is a non-trivial challenge in the study of ultrafast processes that are the subject of two-dimensional electron spectroscopy (2DES) and electron-vibrational spectroscopy (2DEVS). In this talk, I introduce a model system with multiple electronic states and anharmonic potential surfaces in a dissipative environment. Then the multistate quantum hierarchical Fokker-Planck equations are presented as a versatile tool. I explain the basics of 2D ES and 2DEVS and show that how spectra are simulated and viewed.