Direct Current Hopping Conductivity in One—Dimensional Nanometre Systems

A one-dimensional random nanocrystalline chain model is established.A dc electron-phonon-field conductance model of electron tunnelling transfer is set up,and a new dc conductance formula in one-dimensional nanometre systems is derived.By calculationg the dc conductivity,the relationship among the electric field,temperature and conductivity is analysed.and the effect of the crystalline grain size and the distrotion of interfacial atoms on the dc conductance is discussed.The result shows that the nanometre system appears the characteristic of negative differential dependence of resistance and temperature at low temperature.The dc conductivity of nanometre systems varies with the change of electric field and trends to rise as the crystalline grain size increases and to decrease as the distroted degree of interfacial atoms increases.     

Mean Field Analysis of Low–Dimensional Systems

For low–dimensional systems, (i.e. 2D and, to a certain extent, 1D) it is proved that mean–field theory can provide an asymptotic guideline to the phase structure of actual systems. In particular, for attractive pair interactions that are sufficiently “spead out” according to an exponential (Yukawa) potential it is shown that the energy, free energy and, in particular, the block magnetization (as defined on scales that are large compared with the lattice spacing but small compared to the range of the interaction) will only take on values near to those predicted by the associated mean–field theory. While this applies for systems in all dimensions, the significant applications are for d = 2 where it is shown: (a) If the mean–field theory has a discontinuous phase transition featuring the breaking of a discrete symmetry then this sort of transition will occur in the actual system. Prominent examples include the two–dimensional q = 3 state Potts model. (b) If the mean–field theory has a discontinuous transition accompanied by the breaking of a continuous symmetry, the thermodynamic discontinuity is preserved even if the symmetry breaking is forbidden in the actual system. E.g. the two–dimensional O(3) nematic liquid crystal. Further it is demonstrated that mean–field behavior in the vicinity of the magnetic transition for layered Ising and XY systems also occurs in actual layered systems (with spread–out interactions) even if genuine magnetic ordering is precluded.     

Time Asymptotics for Solutions of Vlasov–Poisson Equation in a Circle

We prove that there exists a class of solutions of the nonlinear Vlasov–Poisson equation (VPE) on a circle that converges weakly, as t , to a stationary homogeneous solution of VPE. This behavior is called, in the linear case, Landau damping. The result is obtained by constructing a suitable scattering problem for the solutions of the Vlasov–Poisson problem. A consequence of this result is that a class of stationary solutions of the Vlasov–Poisson equation is unstable in a weak topology.     

Symmetry Classification of the One–Dimensional Second Order Equation of a Hydrodynamic Type

Abstract

The paper contains a symmetry classification of the one–dimensional second order equation of a hydrodynamical type L(Lu)+λLu=F (u), where L ≡ ? _t+u? _x. Some classes of exact solutions of this equation are given.     

Random Motion of a Charged Test Particle with a Classical Constant Velocity in Vacuum in a Cylindrical Spacetime

We examine the random motion of a charged test particle with a nonzero classical velocity driven by quantum electromagnetic vacuum fluctuations in a cylindrical spacetime and calculate both the velocity and position dispersions of the test particle. It is found that the dispersions display different behaviour in different directions. These differences can be understood as a result of the topology of the configuration and initial physical conditions.     

Formation of Singularities in One—Dimensional Hydromagnetic Flow

Two results on the formation of singularities in solutions to the system of one-dimensional hydromagnetic dynamics are presented.In particular,it is shown that shocks form from a smooth spatial periodic flow in a finite time if the initial amounts of entropy and the “magnetic field” in each period are smaller than those of sound waves.A quantitative estimate of blow-up time is also given.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

Simple Method Obtaining Analytical Expressions of Particle and Kinetic—Energy Densities for One—Dimensional Confined Fermi Gases

We develop a simple approach to obtain explicitly exact analytical expressions of particle and kineticenergy densities for noninteracting Fermi gases in one-dimensional harmonic confinement,and in one-dimensional box confinement as well.     

One loop renormalizability of the Poisson–Lie sigma models

We present the proof of the one loop renormalizability in the strict field theoretic sense of the Poisson–Lie σ-models. The result is valid for any Drinfeld double and it relies solely on the Poisson–Lie structure encoded in the target manifold.     

Electronic Structure of One—Dimensional Boron Chains with Density Functional Theory Method

One-dimensional chain structures of Bn(n=6-16) are calculated by employing a 6-311 G^* basis set.The present calculations show that all the chain structures of interest have local minima with large binding energy per atom and short bond length.It is also found that many previous reported structures of B6 and B7 clusters are saddle points and the one-dimensional chain structures are the corresponding ground-state structures of B6 and B7 clusters.     

Dynamic Localization of a One—Dimensional Quantum Dot Array in an ac Electric Field

We investigate the dynamics of two interaction electrons confined to one-dimensional quantum dot array in an ac electric field.We find that initially localized electrons will remain localized in the absence of coulomb interaction if the ratio of the ac field magnitude to the frequency is a root of the ordinary zero-order Bessel function.In contrast to the case without Coulomb interaction,no matter what the value is,the electrons are delocalized and the delocalization effect depends on the ratio U/ω and eaE/ω,where U is the strength of Coulomb interaction,a is the lattice constant,and E and ω are the ac field amplitude and frequency,respectively.     

Global Existence of Classical Solutions to the Inelastic Vlasov–Poisson–Boltzmann System

We study the global existence and uniqueness of classical solutions to the inelastic Vlasov–Poisson–Boltzmann system for a soft potential in the near vacuum regime. For the global existence of classical solutions, we assume reasonable conditions on the restitution coefficient, which represents the character of inelastic collisions. We use the smallness of initial data and an algebraically decaying weight function in the spatial variable to control the self-consistence force and collision operator.     

A Quasi—One—Dimensional Model for a Solar Flux Tube

We develop the quasi-one-dimensional flux tube model with magnetohydrodynamical equations.In order to know whether the magnetic field can maintain their similar structure from photosphere to chromosphere,we suppose that the flux tube is thin in radius relative to the length,and that the quantities in the cross section are averaged.The radii of the flux tube and the magnetic field are numerically simulated.One of the important results shows that the flux tube does not expand as quickly as the existing model when it is out of the photoxphere with high velocity.This is consistent with observations of the magnetic field in the photosphere and chromosphere.     

How to Find Separation Coordinates for the Hamilton–Jacobi Equation: A Criterion of Separability for Natural Hamiltonian Systems

The method of separation of variables applied to the natural Hamilton–Jacobi equation (u/q _i )²+V(q)=E consists of finding new curvilinear coordinates x _i (q) in which the transformed equation admits a complete separated solution u(x)=u _(i)(x _i ;). For a potential V(q) given in Cartesian coordinates, the main difficulty is to decide if such a transformation x(q) exists and to determine it explicitly. Surprisingly, this nonlinear problem has a complete algorithmic solution, which we present here. It is based on recursive use of the Bertrand–Darboux equations, which are linear second order partial differential equations with undetermined coefficients. The result applies to the Helmholtz (stationary Schrödinger) equation as well.     

The Lie–Rinehart Universal Poisson Algebra of Classical and Quantum Mechanics

The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z  =  i z, z  =  0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z  =  0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ .     

On the Violation of Ohm’s Law for Bounded Interactions: a One Dimensional System

We consider an infinite Hamiltonian system in one space dimension, given by a charged particle subjected to a constant electric field and interacting with an infinitely extended system of particles. We discuss conditions on the particle/medium interaction which are necessary for the charged particle to reach a finite limiting velocity. We assume that the background system is initially in an equilibrium Gibbs state and we prove that for bounded interactions the average velocity of the charged particle increases linearly in time. This statement holds for any positive intensity of the electric field, thus contradicting Ohms law.Work partially supported by the GNFM-INDAM and the Italian Ministry of the University.     

Exciton Excitations in a One－Dimensional Band Insulator with Hubbard Interactions

We study the properties of exciton excitations in the Hubbard model with alternating potential and dimerized hopping terms at half filling. With increasing Coulomb repulsive, we find that a spin triplet exciton band develops below the band gap. At certain critical interaction, the excitation gap of this exciton band vanishes and a new phase with a dimerized ground state emerges. The value of this critical Coulomb interaction is determined perturbatively.     

Quantum vs. Classical Integrability in Ruijsenaars–Schneider and Calogero–Moser Systems

The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider (R-S) and Calogero-Moser systems is addressed. The classical Calogero and Sutherland systems (based on any root system) at equilibrium have many remarkable properties; for example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all integer valued. These are related to the energy eigenvalues of the quantum Calogero and Sutherland systems. Similar features and results hold for the R-S type of integrable systems based on the classical root systems.     

Geometrical Method for the Generalized Moore Equations of a One—Dimensional Cavity with Two Moving Mirrors

Extending the approach proposed by Cole and Schieve (1995 Phys.Rev.A 52 4405) for a one-dimensional cavity with one moving mirror,we develop a geometrical method to solve exactly the generalized Moore (GM) equations for a one-dimensional cavity with two moving mirrors.As examples of applying our method,the GM equations are solved in detail when the two mirrors oscillate resonantly,and the dependences of the solutions on the frequency and dephasing of the mirror motions are investigated.