Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Gene admixture in the Silk Road region of China: Evidence from mtDNA and melanocortin 1 receptor polymorphism

Mitochondrial DNA control region segment I sequences and melanocortin 1 receptor (MC1R) gene polymorphism were examined in ethnic populations in the silk road region of China. Both the frequencies of the MC1R variants and the results of mtDNA data in this region presented intermediate values between those of Europe and East and Southeast Asia, which suggested extensive gene admixture in this area and was in general agreement with previous studies. Phylogenetic analysis of the ethnic populations in the Silk Road region that based on mtDNA data didn't show expected cluster pattern according to their ethnogenesis. We suspect that a high migration rate in female among these closely related populations and other three demographic events might account for it.