Effect of local field fluctuations on orientational ordering in random-site dipole systems

Some peculiarities of dipole ordering in systems with uniaxial or cubic anisotropy with an arbitrary degree of dilution are analyzed in terms of random local field theory. The approach takes into account the effect of thermal and spatial fluctuations of the local fields acting on each particle from its neighbors with an accuracy corresponding to that of the Bethe-Paierls pair clusters approach. We show that ferromagnetic (ferroelectric) structure for uniaxial Ising dipoles distributed on a simple cubic lattice is intrinsically unstable against the fluctuations of the local fields for any concentration of the dipoles. This result is quite different from the prediction of the mean-field theory which implies the possibility of ferromagnetic ordering as a metastable state in field-cooled experiments. The local field fluctuations do not exclude, however, antiferromagnetic ordering above a certain critical concentration. Ferromagnetic ordering is possible for other types of lattice geometries and for an amorphous-like dipole distribution above a certain critical concentration. A simple physical explanation of such behavior is given based on the specific angular dependence of the dipole-dipole interaction that results in a relatively high value of the local field second moment for simple cubic lattice.     

各向异性立方晶体的弹性格林函数及其应用

本文计算了各向异性立方晶体的弹性格林函数的级数展开式,给出了直到二级近似的展开式的系数。将所得结果应用于弹性偶极子模型,给出了对称中心所产生的位移场及两对称中心间的弹性相互作用的表示式。应用于Cu,K等强各向异性立方晶体,虽然级数的收敛较慢,但所得关于对称中心的位移场,及二对称中心间的互作用能的数值结果,竟与基于点阵的不连续性作出的点阵静力学计算所得的结果基本一致。从而表明,本文给出的直到二级近似的弹性格林函数的解析表示提供了一个可以普遍应用的简便的方法。它可以较准确地描述立方晶体的某些力学行为。 关键词：     

Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies

We review some of the techniques that lead to the effective medium representation of a three-dimensional (3D) periodic metamaterial. We consider a 3D lattice of lead telluride cubic resonators at mid-infrared (MIR) frequencies. Each cubic resonator is modeled with both an electric and a magnetic dipole, through a method called the dual dipole approximation. The electric and magnetic polarizabilities of a cubic resonator are computed via full-wave simulations by mapping the resonator's scattered field under electric/magnetic excitation only to the field radiated by an equivalent electric/magnetic dipole. We then analyze the allowed modes in the lattice, with transverse polarization and complex wavenumber, highlighting the attenuation that each mode experiences after one free space wavelength. We observe the presence of two modes with low attenuation constant, dominant in different frequency ranges, able to propagate inside the lattice: this allows the treatment of the metamaterial as a homogeneous material with effective parameters, evaluated by using various techniques. We then show that the metamaterial under analysis allows for the generation of artificial magnetism (i.e., relative effective permeability different than unity, including negative permeability with low losses) at MIR frequencies.     

A new class of stationary solutions to the five-dimensional Kaluza-Klein field equations

Using the five-dimensional potential formalism, a set of six new stationary axisymmetric solutions to the Kaluza-Klein field equations are constructed from the one dimensional subspace of the potential space. All the solutions have scalar potential and magnetic field, two of them possess magnetic monopoles and the other describes a magnetic dipole.     

Solitons in a diatomic chain with competing nonlinearities

A one-dimensional diatomic chain whose energy contains cubic and quartic terms in the atomic displacements is considered. A modified asymptotic method is proposed for finding soliton solutions to equations describing systems with nonlinearities of various symmetry. It is shown that the dynamics of the model in question can be described in terms of equations that are similar to the dynamic equations for a diatomic chain with an even potential function. Soliton solutions of a new, unusual type are found in the specific case of a free diatomic chain with a purely cubic anharmonic potential.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices

The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components are described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different ²⁹Si concentrations in magnetic fields directed along three crystallographic axes is considered.     

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.     

Theory of two-photon lasers I

We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Controllable magnetic solitons excitations in an atomic chain of spinor Bose–Einstein condensates confined in an optical lattice

We propose an experimental scheme to show that the nonlinear magnetic solitary excitations can be achieved in an atomic spinor Bose–Einstein condensate confined in a blue-detuned optical lattice. Through exact theoretical calculations, we find that the magnetic solitons can be generated by the static magnetic dipole–dipole interaction (MDDI), of which the interaction range can be well controlled. We derive the existence conditions of the magnetic solitons under the nearest-neighboring, the next-nearest-neighboring approximations as well as the long-range consideration. It is shown that the long-range feature of the MDDI plays an important role in determining the existence of magnetic solitons in this system. In addition, to facilitate the experimental observation, we apply an external laser field to drive the lattice, and the existence regions for the magnetic soliton induced by the anisotropic light-induced dipole–dipole interaction are also investigated.     

New axially symmetric solutions of the Einstein-Maxwell equations

New exact solutions of the algebraic form for the static Einstein-Maxwell equations representing the exterior gravitational field of a massive magnetic dipole are derived. They are then used for construction of the stationary electrovacuum solutions reducing to the Schwarzschild metric in a pure vacuum limit.     

声诱导电磁场的赫兹矢量表示与多极声电测井模拟

在假设声场不受电磁场影响的前提下，将Pride声电耦合方程组化为具有电流源的麦克斯韦方程组.与空间位置固定的电流源产生的电磁场不同，孔隙地层中声波诱导的电磁场是由空间波动的电流源产生的.通过引入赫兹矢量，将求解麦克斯韦方程组问题转化为求解关于赫兹矢量的非齐次矢量赫姆霍兹方程组.通过求解该方程组，得出电磁场表达式.利用此方法，针对声电效应测井，分别计算了由单极声源、偶极声源、四极声源激发的井内声场及其诱导电磁场的全波波形. 关键词： 孔隙介质 诱导电磁场 测井 多极声源     

Superfluidity of a perfect quantum crystal II

This paper continues the work begun in a previous paper [Eur. Phys. J. B 71, 85 (2009)]. To treat the equations that describe a crystal with condensate that can be superfluid, a method termed the Kirkwood approximation is used. Earlier, the method was found to be rather seminal when applied to a classical crystal. In the case of a simple cubic lattice, solutions to the equations under study can be expressed in terms of the well-known Mathieu functions. A more realistic case of the face centered cubic lattice is also considered although in this case the three-dimensional equations cannot be reduced to one-dimensional ones. Condensate crystals without superfluidity are studied first and then the same crystals in a superfluid state. It is shown in particular that a crystal in which the condensate is formed is energetically preferable with respect to the same quantum crystal without condensate at absolute zero of temperature. Therefore, on lowering the temperature there must somewhere occur Bose-Einstein condensation in the crystal. In the concluding section, we discuss various physical aspects of the problem.     

Stationary solutions in five-dimensional general relativity

Asymptotically Minkowskian stationary axisymmetric solutions of the five-dimensional Einstein equations are generated from particular classes of stationary axisymmetric solutions of the four-dimensional Einstein-Maxwell equations. First, the five-dimensional electrostatic and magnetostatic solutions are generated from the four-dimensional electrostatic solutions and a harmonic scalar field. Then, a new class of five-dimensional nonstatic solutions are generated from the four-dimensional class =+1. As an example, a three-parameter family of regular asymptotically flat rotating solutions is constructed. These solutions can be interpreted, after dimensional reduction to four dimensions, as extended elementary particles with mass, spin, electric charge, and magnetic dipole moment.     

Conformal field theory representation and background-independent action for superstring field theory

The two-dimensional conformal field theory representation of Witten's open superstring field theory is discussed. We argue that the previously suggested cubic action for the superstring is actually dependent on the spacetime background, and suggest a modification which formally removes this dependence. The transformation from the new version of the superstring cubic action to Witten's action for open string states is discussed. A class of linearized solutions to the equations of motion of the open superstring cubic action are exhibited. These solutions are in one-to-one correspondence with the physical excitations (both massless and massive) of the open and closed type I superstrings.     

Nonlinear coherent dynamics of an atom in an optical lattice

We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically.