Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes,gap solitons and truncated nonlinear Bloch waves,in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,supported by a combination of linear and nonlinear periodic lattice potentials.The former is found to be stable once placed inside a single well of the nonlinear lattice,it is unstable otherwise.Contrary to the case with constant self-focusing nonlinearity,where the latter solution is always unstable,here,we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices.The practical possibilities for experimental realization of the predicted solutions are also discussed.     

Fluctuation theorems for dielectrics with periodic boundary conditions

We derive fluctuation theorems for dielectrics with periodic boundary conditions defined by a Bravais lattice in which the configuration of a large number of permanent dipoles in the unit cell is repeated periodically. We use the electrostatic approximation and show that it is essential to consider bounded geometry. We consider in particular geometries adapted to the Ewald summation used in computer calculations, namely ellipsoids, with as special cases a slab and a sphere. The fluctuations depend strongly on the chosen geometry.     

Electrodynamics of bounded spatially dispersive media: The additional boundary conditions

The eigenfunction for the center of mass motion of a Mott-Wannier exciton in a bounded medium has been determined by solving asymptotically an effective mass equation, assuming electron and hole reflect perfectly from the surface: the surface potential is taken as an infinite barrier. Using this eigenfunction, the non-local susceptibility was determined. From it the relevant additional boundary condition for this model follows: the total flux associated with the sum of the polarization waves vanishes at the surface.     

A long-range ferromagnetic spin model with periodic boundary conditions

A possible way to study long-range interacting particles in finite–infinite periodic systems is applied to a modified Ising model with ferromagnetic interaction that decays as a 1/r^α law. We verify, by Monte Carlo heat-bath simulations for cases in D dimensions, that the thermodynamic quantities scale in a way proposed by Tsallis, and that the mean field theory is exact in the last model for all 0⩽α⩽D/2 suggested previously by other authors.     

Calculating the pressure in simulations using periodic boundary conditions

Because it is not immediately clear how to write down a proper Hamiltonian for a system in periodic boundary conditions, particularly with Coulombic interactions, we consider a large, finite array of copies of a basic simulation cell containingN particles with some interaction between them. We also putN independent copy particles in each of the copy cells of the array and write down a constrained Lagrangian for the whole system. Constraints on the velocities of the particles of the whole array together with an appropriate initial condition implement the periodic structure in the cells of the array of copies. We derive a Hamiltonian for the whole system with constraints and then derive the equations of motion and a virial expression for the pressure tensor in terms of the forces on the system. In the limit as the array of cell copies becomes large, the equations of motion become the standard ones used in periodic-boundaryconditions simulations. The method also provides an unequivocal algorithm for the pressure in this limit in terms of a virial expression. Particular attention is paid to the case of Coulombic interactions.     

Driven nonequilibrium lattice systems with shifted periodic boundary conditions

We present the first study of a driven nonequilibrium lattice system in the two-phase region, withshifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, we find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.     

扩展Su-Schrieffer-Heeger模型在周期性边界条件下的相变

文章计算了含有三种跃迁项(最近邻(NN)、次近邻(NNN)、次次近邻(NNNN)跃迁项)的扩展Su-Schrieffer-Heeger(SSH)模型(模型ⅰ)的热力学特性.对仅含有二种跃迁项(NN、NNN跃迁项)的扩展SSH模型(模型ⅱ)、仅含有一种跃迁项(NN跃迁项)的SSH模型(模型ⅲ)也作了类似的计算.在低温下,每个模型都有相变且跃迁项的存在会降低相变温度.由于NNN跃迁项的存在,在极低温条件下,关于热容量与温度比(HCOTR)随温度变化的单调性,模型i与其它两个模型存在差异.在低温下,模型ⅰ的HCOTR的单调性,会受NN或NNN或NNNN跃迁项的影响并且NN或NNN跃迁项会影响其相变.     

Asymptotic free energy of a system with periodic boundary conditions

A -dimensional classical particle system in a torus, i.e., in a rectangular box with periodic boundary conditions, is considered in a canonical ensemble. Subject to mild restrictions over and above the usual stability and tempering conditions it is proved that the thermodynamic limit for the torus exists and is identical with that for systems contained in normal domains with boundaries or walls. If, in addition, the pair interaction potential (r) decreases sufficiently rapidly (so thatr(r) is integrable at ), and satisfies some further regularity conditions, then the difference between the free energies of the torus and of the corresponding box is at most of the order of a surface term. Somewhat stronger results are indicated for the grand canonical pressure.     

Threshold conditions and bound states for locally periodic delta potentials

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g _n , n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D ₁(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D ₁(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D ₁(N, g). A similar study is presented for case (b). Using the properties of D ₁(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g _n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.     

Quantum group invariant integrable n-state models with periodic boundary conditions

Using the methods of topological quantum field theory we construct aU _q [sl(n)] invariant integrable transfer matrix for the case ofq being a root of unity. It corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. its interior. By means of the nested Bethe ansatz method we analyse conformai properties and discuss the representational content of the Bethe ansatz solutions.     

Remote two-time boundary conditions and special states in quantum mechanics

For an oscillating universe, the assumptions of wave-function localization and approximate symmetry for the initial and final states impose restrictions on the intermediate motion. We argue that one of these restrictions is the avoidance of superpositions of macroscopically distinct states.     

Stationary states for a mechanical system with stochastic boundary conditions

We consider a system of Newtonian particles, with a long-range repulsive pair potential, moving in a cavity whose surface temperature is spatially varying. When a particle hits the surface, it is thermalized at the temperature of the collision point. We prove that this system has a unique stationary ensemble, to which any initial distribution converges for large times. We show that this stationary ensemble depends continuously on the surface temperature profile.     

Reciprocity principle for radiative transfer models that use periodic boundary conditions

Many numerical models use periodic boundary conditions in solving the radiative transfer through heterogeneous media specified over a fixed domain. A reciprocity principle applicable to solutions from these models is derived for the common situation of a scattering and absorbing heterogeneous medium that is illuminated over the entire domain from a single direction. The derived reciprocity principle states that the domain-averaged bidirectional reflectance distribution function remains invariant when incoming and outgoing directions are interchanged, regardless of the heterogeneity of the medium and the size of the domain. This reciprocity principle provides a simple and useful benchmark test for radiative transfer models that use periodic boundary conditions.     

Optics in spatially dispersive media: The energy theorem and the boundary conditions

The optics of spatially dispersive media is developed starting from a macroscopic material equation in differential form. The energy theorem is reformulated exhibiting the energy density, energy flux and the absorption density of polaritons. The 6 boundary conditions needed at an interface between to spatially dispersive media are derived.     

Mesoscopic quantum properties and the fundamental limit of switching of polarization states of light in spatially periodic systems

Quantum analysis of the nonlinear dynamics and self-switching of unidirectional waves in nonlinear systems with distributed feedback is carried out in the Hartree approximation. Quantum limitations on the observation of self-switching are found for the polarization characteristics of light. The formation of nonclassical mesoscopic states of light is predicted. The phenomenon of optical “superfluidity” in systems with distributed feedback is discussed.     

Self-organized phenomena of pedestrian counter flow in a channel under periodic boundary conditions

In this paper we investigate self-organized phenomena such as lane formation generated by pedestrian counter flow in a channel.The lattice gas model is extended to take the effect of walkers in the opposite direction into account simultaneously when they are in the view field of a walker,i.e.,walkers tend to follow the leaders in the same direction and avoid conflicts with those walking towards them.The improved model is then used to mimic pedestrian counter flow in a channel under periodic boundary conditions.Numerical simulations show that lane formation is well reproduced,and this process is rather rapid which coincides with real pedestrian traffic.The average velocity and critical density are found to increase to some degree with the consideration of view field.     

On the spectral decompositions of the linear transport operator with periodic boundary conditions

It is shown that the linear transport operator for a slab with periodic boundary conditions, or for infinite medium, can be analyzed within the Friedrichs' model of perturbation for non-selfadjoint operators. This leads to rephrasing Case's generalized eigenfunction expansion in terms of Hilbert space operators only.     

Molecular dynamics calculation of the dielectric constant without periodic boundary conditions. I

We outline the difficulties in obtaining a reliable value of the dielectric constant of a fluid using molecular dynamics calculations with periodic boundary conditions, and give some explanation of the observed asymptotic behaviour of h_D (r) and hΔ(r) in Monte Carlo simulations of dipolar hard spheres. An alternative method consisting in simulating a dielectric in vacuum is described. This is applied to two dimensional systems. The pertinent theoretical relations for a dielectric disc in vacuum are therefore derived. It is concluded that relations involving MC or MD computation of <m ²> must be carefully handled.