Soliton and boundary condition induced fractional fermion number

We show that for a fermion in a bounded background potential in a finite box, eigenvalues of the total charge are independent of whether the potential is solitonic and depend only on the boundary condition: half-odd integral or integral for charge conjugation (C) invariant boundary conditions and an arbitrary fraction forC non-invariant boundary conditions. Fractional fermion numbers for infinite space Jackiw-Rebbi and Goldstone-Wilczek Hamiltonians are reproduced in finite space by using boundary conditions different from the periodic ones of Rajaraman and Bell.     

Theory on Morphological Instability in Driven Systems

Motivated by recent findings from simulation of a driven lattice gas under shifted periodic boundary conditions, we study within the context of a continuum model the interfacial stability of driven diffusive systems. In this model, an external driving field maintains the system away from equilibrium. Well below criticality, steady-state solutions of the associated bulk kinetic equation are obtained. Our results successfully account for the novel features found in simulation. In particular, the solution describing a pair of interfaces tilted with respect to the driving field under periodic boundary conditions shows a tilt-dependent bulk density (and internal energy), and boundary layers near one of the interfaces. Focusing on the interface dynamics, one finds that such an interface exhibits a characteristic Mullins-Sekerka instability. This is argued to be responsible for the onset of the single- to multistrip transformation observed in simulation.     

Ab initio molecular dynamics in a finite homogeneous electric field

We treat homogeneous electric fields within density functional calculations with periodic boundary conditions. A nonlocal energy functional depending on the applied field is used within an ab initio molecular dynamics scheme. The reliability of the method is demonstrated in the case of bulk MgO for the Born effective charges, and the high- and low-frequency dielectric constants. We evaluate the static dielectric constant by performing a damped molecular dynamics in an electric field and avoiding the calculation of the dynamical matrix. Application of this method to vitreous silica shows good agreement with experiment and illustrates its potential for systems of large size.     

Yukawa potentials in systems with partial periodic boundary conditions. I. Ewald sums for quasi-two-dimensional systems

Yukawa potentials are often used as effective potentials for systems such as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential; in this small screening limit, or Coulomb limit, the potential is long-ranged. As is well known in computer simulation, a simple truncation of the long-ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of space, has already been derived for the Yukawa potential [Molec. Phys. 88, 1357 (1996); J. Chem. Phys. 113, 10459 (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [J. Chem. Phys. 126, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. Special attention is paid to the Coulomb limit and its relation to the electroneutrality of systems.     

Liquid-vapor interface in liquid binary alloys: an ab initio molecular dynamics study

We report the results of an ab initio molecular dynamics simulation of the liquid-vapor interface of two binary liquid alloys, Na(0.3)K(0.7) and Li(0.4)Na(0.6), whose bulk behavior exhibits rather differing ordering tendencies. The study has been performed using samples of 2000 and 3000 particles, respectively, in a slab geometry with periodic boundary conditions. In both cases, the total ionic density distributions along the normal to the interface display some layering with a virtually pure monolayer of the lower surface tension component located outermost at the interface. However, the two systems behave very differently below the interface which can be accounted for by their different ordering tendencies in the bulk.     

Bosonization rules in 12 + 1 dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

Bosonization rules in dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.     

On the one-dimensional spin-1/2-Chain and its related fermion models

We study the linear anisotropic spin-1/2-Heisenberg model with periodic as well as antiperiodic boundary conditions. Using two assumptions about the eigenvalues of the related fermion models it is shown, how the exactly known energy spectrum of the periodic Heisenberg model is altered in the antiperiodic case. This investigation provides basis for a subsequent test of a Hartree-Fock approximation. It gives fairly good results for the groundstate energy and the energy dispersion of low-lying excitations. Hartree-Fock solutions with gapless excitations yield a qualitatively correct picture of the phase diagram of the Heisenberg model.     

KONDO ANOMALIES OF THE HEAVY FERMION SYSTEMS

The interdependences of the Iow temperature properties in heavy fermion compounds with the Kondo lattice parameters are obtained from a two-conduction band periodic s-f exchange model by using the Green’s function method .The results indicate that the anomalous Iow temperature properties of the specific heat,resistivity and the static magnetic susceptibility in the heavy fermion systems are all the characteristic fea- tures of the Xondo Iattice. The influences of the pressure on the Kondo temperature TX and on the superconducting transition temperature T_C in the heavy fermion systems are also discussed.     

Computer simulation of ionic systems. Influence of boundary conditions

The results of molecular dynamics calculations for systems of charged particles under periodic boundary conditions are reported for the case in which the periodic array of particles makes a macroscopically large sphere surrounded by a continuum of dielectric constant ?′. It is shown that thermodynamic and most dynamic properties are independent of the nature of the surrounding medium. The conductivity σ(ω) of the system depends strongly on the dielectric properties of the surrounding medium.     

Critical boundary sine-Gordon revisited

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in Ref. [J. Polchinski, L. Thorlacius, Phys. Rev. D 50 (1994) 622]. We find that the entire SL (2, C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strong–weak coupling generalization of T-duality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the self-dual radius. These have simple expression in fermion variables. We postulate sine-Gordon-like field theories with discrete gauge symmetries for which they are the appropriate boundary states.     

Model fermion Monte Carlo with correlated pairs. II

We study the fundamental challenge of fermion Monte Carlo for continuous systems: the fermion “sign problem.” In particular, we describe methods that depend upon the use of correlated dynamics for ensembles of correlated sets of walkers that carry opposite signs. We explain the concept of marginally correct dynamics, and show that marginally correct dynamics that produce a stable overlap with an antisymmetric trial function give the correct fermion ground state. Many-body harmonic oscillator problems are particularly tractable: their stochastic dynamics permits the use of regular geometric structures for the ensembles, structures that are stable when appropriate correlations are introduced, and avoid the decay of signal-to-noise that is a normal characteristic of the sign problem. This approach may be a guide in the search for algorithmic approaches to calculations of physical interest.     

An efficient parallel algorithm for non-equilibrium molecular dynamics simulations of very large systems in planar Couette flow

In this paper we present an efficient parallel domain decomposition algorithm for non-equilibrium molecular dynamics (NEMD) simulations of large systems under planar Couette flow. We propose a modified deforming cell method that permits NEMD simulations with negligible penalties due to the Lees-Edwards periodic boundary conditions. The algorithm was used to study large systems of the Weeks-Chandler-Andersen fluid in order to obtain better viscosity results at the low shear rate regimes where the signal-to-noise ratio is very small.     

Fluctuation theorems for dielectrics

We discuss fluctuation theorems for dielectrics from a unified point of view. A simple susceptibility theorem is proven for a uniform dielectric contained in a vessel with ideally conducting walls of arbitrary shape. Also we derive a theorem for systems with periodic boundary conditions. The latter is of interest for molecular dynamics calculations on polar dielectrics.     

A new boundary condition for simulations of systems with charge-charge interactions

We introduce a new boundary condition for simulation of charged systems which is a generalization of periodic boundary conditions and reduces the long-range correlations inherent in periodic boundary conditions. An effective pair potential is calculated for the new condition.     

Thermodynamical and Green function many-body Wick theorems

The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. “Many-body” means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same “time” (in the interaction representation). The method of proving is based on: 1) the first-order differential equation of Schwinger type for: 1a) -product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n −1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems.     

Analysis of a Lennard-Jones fcc structure melting to the corresponding frozen liquid: Differences between the bulk and the surface

We computed a Lennard-Jones frozen liquid with a free surface using classical molecular dynamics. The structure factor curves on the free surface of this sample were calculated for different depths knowing that we have periodic boundary conditions on the other parts of the sample. The resulting structure factor curves show an horizontal shift of their first peak depending on how deep in the sample the curves are computed. We analyze our resulting curves in the light of spatial correlation functions during melting. The conclusion is that the differences between bulk and surface are quite small during melting and that at the end of melting, only the very surface happens to be less dense than the bulk. This result is intrinsic to the shape of the Lennard-Jones potential and does not depend on any other parameter.