Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorised in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual Newtonian-like terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the electronic friction. Possible ways of calculating the friction forces which are shown to be given via complicated non-equilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green's functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions. This work also generalises previous attempts, mostly based on model systems, of introducing the electronic friction into Molecular Dynamics equations of atoms.Comment: 18 page

Magnetic friction due to vortex fluctuation

We use Monte Carlo and molecular dynamics simulation to study a magnetic tip-sample interaction. Our interest is to understand the mechanism of heat dissipation when the forces involved in the system are magnetic in essence. We consider a magnetic crystalline substrate composed of several layers interacting magnetically with a tip. The set is put thermally in equilibrium at temperature T by using a numerical Monte Carlo technique. By using that configuration we study its dynamical evolution by integrating numerically the equations of motion. Our results suggests that the heat dissipation in this system is closed related to the appearing of vortices in the sample.Comment: 6 pages, 41 figure

Class of dilute granular Couette flows with uniform heat flux

In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad's moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad's method, the agreement being only qualitative in the case of the kinetic model.Comment: 15 pages, 10 figures; v2: change of title plus some other minor change

The Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls

Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes hydrodynamic modeling of dilute granular gases of monodisperse particles that collide nearly elastically. The Knudsen temperature jump manifests itself as an additional term, proportional to the temperature gradient, in the boundary condition for the temperature. Up to a numerical pre-factor of order unity, this term is known from kinetic theory of elastic gases. We determine the previously unknown numerical pre-factor by measuring, in a series of molecular dynamics (MD) simulations, steady-state temperature profiles of a gas of elastically colliding hard disks, confined between two thermal walls kept at different temperatures, and comparing the results with the predictions of a hydrodynamic calculation employing the modified boundary condition. The modified boundary condition is then applied, without any adjustable parameters, to a hydrodynamic calculation of the temperature profile of a gas of inelastic hard disks driven by a thermal wall. We find the hydrodynamic prediction to be in very good agreement with MD simulations of the same system. The results of this work pave the way to a more accurate hydrodynamic modeling of driven granular gases.Comment: 7 pages, 3 figure

Molecular dynamics simulation of polymer helix formation using rigid-link methods

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under gradual cooling are followed until each reaches a state from which no further change is possible. The interactions are chosen so that the true ground state is a helix, and a high proportion of simulation runs succeed in reaching this state; the fraction that manage to form defect-free helices is a function of both chain length and cooling rate. In order to demonstrate behavior analogous to the formation of protein tertiary structure, additional attractive interactions are introduced into the model, leading to the appearance of aligned, antiparallel helix pairs. The simulations employ a computational approach that deals directly with the internal coordinates in a recursive manner; this representation is able to maintain constant bond lengths and angles without the necessity of treating them as an algebraic constraint problem supplementary to the equations of motion.Comment: 15 pages, 14 figure

Exciton correlations in coupled quantum wells and their luminescence blue shift

In this paper we present a study of an exciton system where electrons and holes are confined in double quantum well structures. The dominating interaction between excitons in such systems is a dipole - dipole repulsion. We show that the tail of this interaction leads to a strong correlation between excitons and substantially affects the behavior of the system. Making use of qualitative arguments and estimates we develop a picture of the exciton - exciton correlations in the whole region of temperature and concentration where excitons exist. It appears that at low concentration degeneracy of the excitons is accompanied with strong multi-particle correlation so that the system cannot be considered as a gas. At high concentration the repulsion suppresses the quantum degeneracy down to temperatures that could be much lower than in a Bose gas with contact interaction. We calculate the blue shift of the exciton luminescence line which is a sensitive tool to observe the exciton - exciton correlations.Comment: 27 pages in PDF and DVI format, 8 figure

Effect of bond lifetime on the dynamics of a short-range attractive colloidal system

We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time $\tau$ diverges as the packing fraction $\phi$ approaches a threshold related to percolation, while for short-lived bonds, the $\phi$-dependence of $\tau$ is more typical of a glassy system. At intermediate bond lifetimes, the $\phi$-dependence of $\tau$ is driven by percolation at low $\phi$, but then crosses over to glassy behavior at higher $\phi$. We also study the wavevector dependence of the percolation dynamics.Comment: Revised; 9 pages, 9 figure

Generalized quantum cumulant dynamics

A means of unifying some semiclassical models of computational chemistry is presented; these include quantized Hamiltonian dynamics, quantal cumulant dynamics, and semiclassical Moyal dynamics (SMD). A general method for creating the infinite hierarchy of operator dynamics in the Heisenberg picture is derived together with a general method for truncation (or closure) of that series, and in addition, we provide a simple link to the phase space methods of SMD. Operator equations of arbitrary order may be created readily, avoiding the tedious algebra identified previously. Truncation is based on a simple recurrence formula which is related to, but avoids the more complex contractions of, Wick's theorem. This generalized method is validated against a number of trial problems considered using the previous methods. We also touch on some of the limitations involved using such methods, noting, in particular, that any truncation will lead to a state which is in some sense unphysical. Finally, we briefly introduce our quantum algebra package QuantAL which provides an automated method for the generation of the required equation set, the initial conditions for all variables from any start, and all the higher order approximations necessary for truncation of the series, at essentially arbitrary order

Statistical Properties of Contact Maps

A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of N amino acids, represented by (N-1)-step self avoiding walks on a lattice, grows exponentially with N for all dimensions D>1. We carry out exact enumerations in D=2 on the square and triangular lattices for walks of up to 20 steps and investigate various statistical properties of contact maps corresponding to such walks. We also study the exact statistics of contact maps generated by walks on a ladder.Comment: Latex file, 15 pages, 12 eps figures. To appear on Phys. Rev.