Hierarchical quantum master equation with semiclassical Drude dissipation

We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an improved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple modification but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two--level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. We also present a criterion, which depends only on the system--bath coupling strength, characteristic bath memory time, and temperature, to estimate the performance of the hierarchical quantum master equation.Comment: 10 pages, 8 figures, submitted to J. Chem. Phys. on 2009-08-0

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron transfer rate processes

In this work, we revisit the electron transfer rate theory, with particular interests in the distinct quantum solvation effect, and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem. {\bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier-crossing to tunneling, and from barrierless to quantum barrier-crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.Comment: 13 pages, 10 figures, submitted to J. Phys. Chem.

Electron transfer theory revisit: Quantum solvation effect

The effect of solvation on the electron transfer (ET) rate processes is investigated on the basis of the exact theory constructed in J. Phys. Chem. B Vol. 110, (2006); quant-ph/0604071. The nature of solvation is studied in a close relation with the mechanism of ET processes. The resulting Kramers' turnover and Marcus' inversion characteristics are analyzed accordingly. The classical picture of solvation is found to be invalid when the solvent longitudinal relaxation time is short compared with the inverse temperature.Comment: 5 pages, 3 figures. J. Theo. & Comput. Chem., accepte

Numerical simulation of pressure pulse decay experiment on crushed low permeability rocks considering Klinkenberg effect and gas absorption/desorption

Pressure pulse decay method is widely used for permeability tests for low permeability rock plug samples. This method can be used for crushed grain samples by removing the downstream chamber in standard pulse decay tests. Processes in pulse decay tests for low permeability crushed shale are investigated using numerical simulation. Both the Klinkenberg slip effect for gas flows in low permeability rock and the gas absorption/desorption in the porous matrix are considered. The complete mathematical model is set up to include the two effects. Deviation of the numerical pulse decay curve from the analytical one with an assumption that the pressure keeps a constant in the porous sample is investigated. The relative importance of gas absorption/desorption and gas compressibility is also investigated quantitatively. According to the present investigation, gas compressibility and adsorption both make negative contributions to the permeating process. A potential two-curve method is proposed to decide absolute permeability and the Klinkenberg coefficient when these two parameters cannot be distinguished using one pulse decay curve during the inverse fitting procedure. These two parameters can be determined at the same time only if the experiment is conducted under big initial pressure difference and the Klinkenberg coefficient has at least the same order of magnitude as the pressure

Advancing hierarchical equations of motion for efficient evaluation of coherent two-dimensional spectroscopy

To advance hierarchial equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg--Schrodinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focus on the effects of intermolecular transfer coupling and bi-exciton interaction

Effective solid-to-fluid heat transfer coefficient in EGS reservoirs

The present work developed a three-equation local thermal non-equilibrium model to predict the effective solid-to-fluid heat transfer coefficient in the enhanced geothermal system reservoirs based on the volume averaging method. Due to the high rock-to-fracture size ratio, the solid thermal resistance effect in the internal rocks cannot be neglected in the effective solid-to-fluid heat transfer coefficient. The present three-equation local thermal non-equilibrium model can consider the dynamic variation of the solid thermal resistance in transient heat transfer by introducing the penetration temperature difference. The model was validated by comparison with pore-scale numerical simulations and macro-scale LTNE model numerical simulations. The results show that the three-equation local thermal non-equilibrium model has a high accurac