Ising自旋S=1,具有次近邻相互作用的面心立方格子的反铁磁体在外场下的基态能量

本文用文献[4]中提出的方法,变S=1的Ising体系成一个粒子数不守恒的费密体系,严格地求得了具有最近邻及次近邻相互作用的反铁磁Ising晶格在任意外场下的基态能量,得到了零温的相图。 关键词：     

Reversible random sequential adsorption of dimers on a triangular lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca2+ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.     

Development of a method for modeling the dynamics of many Coulomb particles

An investigation is made of the properties of a new algorithm for numerically solving the Newton equations for many Coulomb particles, based on taking more accurate account of the time dependence of the interaction forces between nearest neighbors. It is shown that when the four nearest neighbors are taken into account the accuracy of the method is considerably increased over that of the previously used method where the two nearest neighbors were included. The accuracy is investigated by monitoring the conservation of energy and by the method of reversing the particle motion (the reversal method). It is shown that the reversibility of the numerical solution is maintained for times of the order of the transit time for the average interparticle distance, whereas the energy is conserved for much longer times with an accuracy of better than a tenth of one percent. A method for diagnosing bound states is proposed from the energy distribution of the mutually nearest neighbors in the center of mass system. A discussion is given of the relationship between the results obtained and the present ideas on the stochastic properties of dynamic systems. It is suggested that the effect of recombination being frozen, discovered from the modeling, results from the absence of Gibbs mixing of the free and bound states.General Physics Institute, Russian Academy of Sciences, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 44–56, November, 1993.     

On the behavior of indicators of melting: Lennard-Jones system in the vicinity of the phase transition

Various indicators of melting for a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The behavior of the radial distribution function g(r) and the associated criteria of melting, modified Lindemann criterion, and criteria based on the properties of short-range orientational order (rotational invariants q _l and w _l of various orders l) has been analyzed in detail in the vicinity of the melting phase transition. A parameter based on the loss of the nearest neighbors of an atom/particle has been proposed to characterize the melting transition. All considered indicators of melting for the Lennard-Jones system have been compared. It has been shown that the indicators of melting derived from the properties of the short-range orientational order are much more sensitive to the melting phase transition and can be used to construct new phenomenological criteria of melting similar to the Lindemann criterion. An additional important advantage of such indicators is the relatively small number of configurations of the system necessary for their calculation.     

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.     

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest–neighbor probability distribution function, \(p_1(r)\), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest–neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of \(p_1(r)\) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest–neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.     

Kohn anomalies in momentum dependence of magnetic susceptibility of some three-dimensional systems

We study a question of the presence of Kohn points, yielding at low temperatures nonanalytic momentum dependence of magnetic susceptibility near its maximum, in electronic spectra of some threedimensional systems. In particular, we consider a one-band model on face-centered cubic lattice with hopping between the nearest and next-nearest neighbors, which models some aspects of the dispersion of ZrZn₂, and the two-band model on body-centered cubic lattice, modeling the dispersion of chromium. For the former model, it is shown that Kohn points yielding maxima of susceptibility exist in a certain (sufficiently wide) region of electronic concentrations; the dependence of the wave vectors, corresponding to the maxima, on the chemical potential is investigated. For the two-band model, we show the existence of the lines of Kohn points, yielding maximum susceptibility, whose position agrees with the results of band structure calculations and experimental data on the wave vector of antiferromagnetism of chromium.     

Mean-Field Dynamics: Singular Potentials and Rate of Convergence

We consider the time evolution of a system of N identical bosons whose interaction potential is rescaled by N ⁻¹. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the mean-field limit N → ∞ the quantum N-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum N-body dynamics to the Hartree dynamics.     

Molecular conformation in molten and glassy polymers

As a consequence of enthalpy fluctuations in a small thermodynamic system, the conformation in molten and glassy polymers is predicted to be more nearly an irregularly folded molecule with 5 to 10 nearest neighbors than a random coil with 50 to 100 nearest neighbors.     

A Spatial Stochastic Model for Rumor Transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate λ. At rate α a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.     

Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states

At high densities and low temperatures, the conventional Widom test particle method to compute the chemical potential of a system of particles with excluded volume interactions fails owing to bad statistics. A way to circumvent this problem is the use of expanded ensemble simulation techniques or thermodynamic integration. In this article, we will describe an alternative method to compute the chemical potential which is conceptually much easier, by computing the density of states of systems of N and N + 1 particles directly; and by performing a test particle simulation at very high temperature. The advantage of our technique is that the densities of states of the N and N + 1 particle system are computed in an ensemble in which particles can pass each other, resulting in a more efficient sampling. We will demonstrate our method not only for single particles but also for chain molecules with intramolecular interactions. By using an infinite temperature expansion and an extension of the density of states to very high energies, we will show that it is also possible to compute the chemical potential without having to compute the density of states for the N + 1 particle system.     

Travelling Waves in a Chain¶of Coupled Nonlinear Oscillators

In a chain of nonlinear oscillators, linearly coupled to their nearest neighbors, all travelling waves of small amplitude are found as solutions of finite dimensional reversible dynamical systems. The coupling constant and the inverse wave speed form the parameter space. The groundstate consists of a one-parameter family of periodic waves. It is realized in a certain parameter region containing all cases of light coupling. Beyond the border of this region the complexity of wave-forms increases via a succession of bifurcations. In this paper we give an appropriate formulation of this problem, prove the basic facts about the reduction to finite dimensions, show the existence of the ground states and discuss the first bifurcation by determining a normal form for the reduced system. Finally we show the existence of nanopterons, which are localized waves with a noncancelling periodic tail at infinity whose amplitude is exponentially small in the bifurcation parameter. Received: 10 September 1999 / Accepted: 15 December 1999     

Dynamics of colloidal crystals

We study the lattice dynamics of colloidal crystals on the assumption that the potential interactions are limited to nearest neighbors and next nearest neighbors and that the long range hydrodynamic interactions may be treated in point approximation. We show that this does not lead to satisfactory agreement with existing experimental data.     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

Travelling Breathers with Exponentially Small Tails in a Chain of Nonlinear Oscillators

We study the existence of travelling breathers in Klein-Gordon chains, which consist of one-dimensional networks of nonlinear oscillators in an anharmonic on-site potential, linearly coupled to their nearest neighbors. Travelling breathers are spatially localized solutions which appear time periodic in a referential in translation at constant velocity. Approximate solutions of this type have been constructed in the form of modulated plane waves, whose envelopes satisfy the nonlinear Schrödinger equation (M. Remoissenet, Phys. Rev. B 33, n.4, 2386 (1986), J. Giannoulis and A. Mielke, Nonlinearity 17, p. 551–565 (2004)). In the case of travelling waves (where the phase velocity of the plane wave equals the group velocity of the wave packet), the existence of nearby exact solutions has been proved by Iooss and Kirchgässner, who have obtained exact solitary wave solutions superposed on an exponentially small oscillatory tail (G. Iooss, K. Kirchgässner, Commun. Math. Phys. 211, 439–464 (2000)). However, a rigorous existence result has been lacking in the more general case when phase and group velocities are different. This situation is examined in the present paper, in a case when the breather period and the inverse of its velocity are commensurate. We show that the center manifold reduction method introduced by Iooss and Kirchgässner is still applicable when the problem is formulated in an appropriate way. This allows us to reduce the problem locally to a finite dimensional reversible system of ordinary differential equations, whose principal part admits homoclinic solutions to quasi-periodic orbits under general conditions on the potential. For an even potential, using the additional symmetry of the system, we obtain homoclinic orbits to small periodic ones for the full reduced system. For the oscillator chain, these orbits correspond to exact small amplitude travelling breather solutions superposed on an exponentially small oscillatory tail. Their principal part (excluding the tail) coincides at leading order with the nonlinear Schrödinger approximation.     

On a kinetic equation for and the dynamical friction of a particle in a plasma-a phenomenological approach

Based on phenomenological considerations, a one particle distribution function consisting of two parts accounting for the effects of “distant” particles and the “nearest” neighbors is suggested. Employing the above distribution function and the Liouville theorem, dynamical friction of a particle in, and a kinetic equation for a plasma are demonstrated.     

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.     

Some consequences of electronic topological transition in 2D system on a square lattice: Excitonic ordered states

We study in a mean-field approximation the ordered “excitonic” states which develop around the quantum critical point (QCP) associated with the electronic topological transition (ETT) in a 2D electron system on a square lattice. We consider the case of hopping beyond nearest neighbors when ETT has an unusual character. We show that the amplitude of the order parameter (OP) and of the gap in the electron spectrum increase with increasing the distance from the QCP, , where and n is an electron concentration. Such a behavior is different from the ordinary case when OP and the gap decrease when going away from the point which is a motor for instability. We show that the chemical potential lies always inside the gap for wavevectors in a proximity of whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybridization effect in the vicinity of two different SP's. The shape of the spectrum as a function of and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high- cuprates. We discuss also details about the phase diagram and the behaviour of the density of states. Received 9 June 1999     

Atomic displacements due to interstitial hydrogen in Cu and Pd

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of 7.36% and 4.3% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion ΔV/V = 0.177 for Cu and 0.145 for Pd.      

Study of one-dimensional nonlinear lattice

In this article a brief review of the theory of one-dimensional nonlinear lattice is presented. Special attension is paid for the lattice of particles with exponential interaction between nearest neighbors (the Toda lattice). The historical exposition of findings of the model system, basic equations of motion, special solutions, and the general method of solutions are given as chronologically as possible. Some reference to the Korteweg-de Vries equation is also given. The article consists of three parts. Firstly, the idea of dual system is presented. It is shown that the roles of masses and springs of a harmonic linear chain can be exchanged under certain condition without changing the eigenfrequencies. Secondly, the idea is applied to the anharmonic lattice and an integrable lattice with exponential interaction force between adjacent particles is obtained. Special solutions to the equations of motion and general method of solution are shown. In the last part, some studies on the Yang-Yang’s thermodynamic formalism is given.