Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2–3%.     

Rate determining factors in protein model structures

Previous research has shown a strong correlation of protein folding rates to the native state geometry, yet a complete explanation for this dependence is still lacking. Here we study the rate-geometry relationship with a simple statistical physics model, and focus on two classes of model geometries, representing ideal parallel and antiparallel structures. We find that the logarithm of the rate shows an almost perfect linear correlation with the "absolute contact order", but the slope depends on the particular class considered. We discuss these findings in the light of experimental results.     

Tests of a trap-controlled hopping model for PVK

A recent model for the Coulomb-trap controlled hopping mobility in PVK has been tested by mobility and permittivity measurements between -70 and +80°C. The key assumption of the model, viz. a discontinuity in the permittivity and Poole-Frenkel coefficient, has been verified. Some of the previously derived parameters have been revised.     

Breakdown of the resistor-network model for steady-state hopping conduction

Master equations are used to study steady-state hopping in a disordered solid. We express each site's occupancy in terms of its quasi-electrochemical potential (QECP); currents flow between sites whose QECP's differ. Coupled nonlinear circuit equations result from the steady-state condition and a boundary condition. When site-to-site QECP differences are much smaller than the thermal energyk _B T, the effect of current flow on occupancies is ignorable, and the equations reduce to those of a resistance network. But this resistor-network model fails: a) at low temperatures, b) with increasing disorder, and c) with increasing emf. We therefore study hopping conduction beyond this approximation. Exactly soluble examples show the importance of current-induced charge redistribution in non-ohmic steady-state flow.     

Diffusive motion in a model for particle hopping

The diffusive motion of adsorbates on crystal planes is studied by means of a lattice gas model with stochastic dynamics, in the disordered phase and at half coverage. The diffusion coefficient and the time-correlation functions measured in field-emission experiments are calculated. These correlation functions are shown to have the proper hydrodynamic power law decay at long times. It is pointed out that if experiments are done at times before the onset of the hydrodynamic regime the value of the diffusion coefficient obtained will be too small. Our results show also that correlations among the adsorbed particles persist for times longer than predicted by a hydrodynamical approximation.     

Mean-field HP model, designability and alpha-helices in protein structures

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with a large number of switchbacks between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha helices.     

Ferromagnetism in the two-dimensional Hubbard model with long-range hopping

The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t _ij ～ ? q ^Ri?Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q _c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.     

Exact solution of the one-dimensional fermionic model with correlated hopping

We extend the Bethe Ansatz solution of a onedimensional integrable fermionic model with correlated hopping to the parameter regime Δ t > 1. It is found that the model is equivalent to one with interaction 2 ? Δ t, but with twisted boundary conditions. Apart from the ground state energy we investigate the low-lying excitations and the asymptotic behaviour of the correlation functions. As in the ease of Δt < 1 we find dominating superconducting correlations for small doping. The behaviour in this regime therefore differs from that of the non-integrable model with symmetric bond-charge interaction (Hirsch model).     

The semi-classical hopping model of the electrical conductivity of semiconductors

A model of localized carriers moving in a hopping manner from one crystallographic point to a neighbouring one is the starting point for the model presented here for the electrical conductivity in semiconductors. An effort is made to link this hopping type of motion of carriers with their mean uniform motion in the crystal. With an assumed shape for the potential barrier for a single hop of a carrier, the model permits the calculation of the effective mass, the mobility of a carrier with energy E, the mean mobility of all carriers in the band, and the electrical conductivity as a function of temperature, T. The model is presented and exemplified by a one-dimensional system.     

可积开边界条件下的 q 形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型,得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础.     

Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

Periodic one-dimensional hopping model with one mobile directional impurity

Analytic solution is given in the steady-state limitt for the system of master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of master equations leads naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasiwalker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasiparticle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.     

An exactly solvable model of the phonon-assisted hopping dc conductivity

The model, which is commonly used to obtain the Mott law for the temperature dependence of the dc conductivity of elemental covalent amorphous semiconductors, is solved exactly in the case of small electron-phonon coupling. Differences between the Mott law and our solution are discussed.