Green functions of the anisotropic Heisenberg model

The Green functions of the anisotropic Heisenberg model are studied by a method which was applied previously to the reduced density matrices. Integral equations are used to prove the existence of the infinite volume limit of the Green functions, and some analyticity properties with respect to the fugacity (or magnetic field), the potentials, and the complex times.Research supported by the National Science Foundation.     

Classical and quantum kinetic equations with exact conservation laws

Stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations. The local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure. For pairwise additive forces conditions on the closure of the one- and two-particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices. To illustrate the nature of these conditions, a closure approximation suitable for a quantum gas is given, yielding an extension of the time-dependent Hartree-Fock equations for the dynamics of a nuclear fluid to include collisions.     

A time convolution less density matrix approach to the nonlinear optical response of a coupled system-bath complex

Time convolution less density matrix theory (TCL) is a powerful and well established tool to investigate strong system-bath coupling for linear optical spectra. We show that TCL equations can be generalised to the nonlinear optical response up to a chosen order in the optical field. This goal is achieved via an time convolution less perturbation scheme for the reduced density matrices of the electronic system. In our approach, the most important results are the inclusion of a electron-phonon coupling non-diagonal in the electronic states and memory effects of the bath: First, the considered model system is introduced. Second, the time evolution of the statistical operator is expanded with respect to the external optical field. This expansion is the starting point to explain how a TCL theory can treat the response up to in a certain order in the external field. Third, new TCL equations, including bath memory effects, are derived and the problem of information loss in the reduced density matrix is analysed. For this purpose, new dimensions are added to the reduced statistical operator to compensate lack of information in comparison with the full statistical operator. The theory is benchmarked with a two level system and applied to a three level system including non-diagonal phonon coupling. In our analysis of pump-probe experiments, the bath memory is influenced by the system state occupied between pump and probe pulse. In particular, the memory of the bath influences the dephasing process of electronic coherences developing during the time interval between pump and probe pulses.     

Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

By stereographically projecting the spin vector onto a complex plane in the equations of motion for a continuum Heisenberg spin chain with an anisotropy (an easy plane and an easy axis) and an external magnetic field, the effect of the magnetic field for integrability of the system is discussed. Then, introducing an auxiliary parameter, the Lax equations for Darboux matrices are generated recursively. By choosing the constants, the Jost solutions are satisfied the corresponding Lax equations. The exact soliton solutions are investigated, then the total magnetic momentum and its z-component are obtained. These results show that the solitary waves depend essentially on two velocities which describe a spin configuration deviating from a homogeneous magnetization. The depths and widths of solitary waves vary periodically with time. The center of an inhomogeneity moves with a constant velocity, while the shape of soliton also changes with another velocity and this shape is not symmetrical with respect to the center. The total magnetic momentum and its z-component vary with time.     

Diffusion modeling of an HF argon plasma discharge in a magneticfield

Using the basic moment equations (number density, flow density, and energy density) for singly ionized argon and for electrons, a simple diffusion equation (essentially one proposed by Lieberman and Lichtenberg, 1994) is adopted (by comparison with experiment), together with an integrated power balance equation. The effects of scaling magnetic field and radius are then discussed first for simple cylinders, for which there are known analytic diffusion solutions. For specific cases having the more complicated geometry of two abutting coaxial cylinders with considerably different radii, the numerical results are well approximated and delimited by considering only the wider cylinder for low magnetic field, and at high magnetic field, where end effects dominate, using the total length and the smallest diameter of the system     

Quantum information transmission between two qubits through an intermediary photon gas

The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.     

The Role of Magnetic Field in Anisotropic String Cosmological Model

In this paper we consider a spatially homogenous and anisotropic Bianchi type-V space-time model to investigate the effects of a magnetic field in string cosmology. We assume that the string’s direction and magnetic field are along x-axis. The field equations are solved by using the equation of state for a cloud of strings and variable magnetic permeability. We derive exact solutions for three types of strings: (i) Nambu strings, (ii) string model where the sum of energy density and string tension density is zero and (iii) Takabayasi strings. We examine the behaviour of scale factors and other physical parameters with and without magnetic field and it is found that the magnetic field effects the dynamics of the universe at early time. During late time the universe becomes isotropic even in the presence of magnetic field. The universe expands with decelerated rate during early stages of the evolution of the universe but it goes to marginal inflation at late times.     

Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

Summary A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.     

Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.     

Pattern of the induced magnetic field in high-temperature superconducting ceramics

Our experiments performed earlier have shown that, when an external magnetic field is absent, the transport critical current in 3-d superconducting ceramics is a homogeneous function of the sample transverse sizes. The transport critical current density and magnetic field induced by the current are homogeneous functions of a point on the sample cross-section. Using these experimental results equations describing the induced magnetic field pattern in ceramic sample have been derived. The distributions of the transport critical current density and induced magnetic field in the samples having polygonal, diamond-shaped cross-sections illustrate the results.     

高温超导YBCO薄膜中的传输交流损耗

基于Norris方程和Bean临界态模型,考虑薄膜超导体内的磁场和电流密度分布特性,通过解析求解的方法推导出薄膜超导体在传输外加电流时其内部的磁场和电流密度以及传输交流损耗的解析表达式,从定量的角度研究超导体截面几何形状对传输交流损耗的影响.结果表明薄膜超导体边缘处的剧烈变化的磁场和电流的分布以及无场区的电流承载能力是...     

The use of polarized coordinates for solving the macroscopic equations of collisionless plasma

A method is developed for the iterative solution of an infinite system of moment equations derived from the collisionless Boltzmann (Vlasov) equation. Since in a strong magnetic field the dominant terms of these equations have a complicated form, the iterative solution after a few steps comes up against difficulties connected with the inversion of matrices of high order. It is found that the transformation of moment equations into the natural polarized coordinate system (Buneman O.: Phys. Fluids4 (1961), 669) diagonalizes the dominant matrices in the magnetic fields with straight lines of force exactly and in adiabatic magnetic fields approximately. In addition, this transformation reveals the symmetries of the moment equations which in some cases permit an exact solution to be found. Apart from the first three moment equations (the equation of continuity, the dynamic (Euler) equation, the equation for pressure) the general moment equation of then-th order is also derived in the Cartesian and general curvilinear coordinate system and in the corresponding polarized natural coordinate systems. The paper deals with some special cases of natural polarized coordinate systems belonging to a magnetic field with straight lines of force (plane, cylindrical and spherical geometry) and with curved lines of force (magnetic trap with mirrors).     

大耦合孔同轴输出腔的3维解析分析

 在高功率微波器件中，通常采用大耦合孔的同轴微波输出腔，该腔为3维结构。采用场等效原理将腔体、耦合孔及其输出负载(行波边界)进行分区,每个区域中的场由界面上的磁流密度决定。采用格林函数积分法可得每个区域中的3维场,再由各个区域的场匹配方程求得腔体的谐振频率、特性阻抗、有载品质因数、模式分布等参数。为腔体的计算和设计提供一种计算模型。     

Emission spectra and intrinsic optical bistability in a two-level medium

Scattering of resonant radiation in a dense two-level medium is studied theoretically accounting for local field effects and renormalisation of the resonance frequency. Intrinsic optical bistability is viewed as switching between different spectral patterns of fluorescent light controlled by the incident field strength. Response spectra are calculated analytically for the entire hysteresis loop of atomic excitation. The equations to describe the non-linear interaction of an atomic ensemble with light are derived from the Bogolubov-Born-Green-Kirkwood-Yvon hierarchy for reduced single particle density matrices of atoms and quantised field modes and their correlation operators. The spectral power of scattered light with separated coherent and incoherent constituents is obtained straightforwardly within the hierarchy. The formula obtained for emission spectra can be used to distinguish between possible mechanisms suggested to produce intrinsic bistability in experiments.     

螺旋型爆磁压缩发生器初始电性能的高频分析

 从电流扩散方程和磁扩散方程出发，研究了在瞬态过程中螺旋型爆磁压缩发生器(HMFCG)的电流密度在螺线管导线中的分布以及感应电流密度在金属套筒中的分布情况，分析计算了爆磁回路初始充电过程中频率对HMFCG电感和电阻的影响，计算结果与实验测量吻合；这为进一步完善校正程序，更好地描述爆磁压缩过程奠定了基础。     

Ionization formation of plasma inhomogeneity by the near-zone field of a magnetic-type source in a magnetized plasma

An investigations is made of the steady-state structure of a plasma inhomogeneity arising as a result of high-frequency heating and additional ionization of a background magnetized plasma by the near-zone field of a magnetic-type source (ring electric current). It is assumed that the source axis is parallel to an external magnetic field; the source frequency belongs in the low hybrid band. The main attention is focused on the particular case (important for possible applications) when the characteristic longitudinal and transverse scales of density distribution considerably exceed the corresponding scales of distribution of the electron temperature and of the source field. Simplified equations for the near-zone field of the source, the electron temperature, and the plasma density are written for this particular case. Based on the numerical solution of these equations, steady-state distributions of plasma parameters in the formed plasma inhomogeneity are found. It is demonstrated that a plasma inhomogeneity proves to be markedly extended along the external magnetic field. It is found that, for the values of the source current that are attainable under the conditions of active ionospheric and model laboratory experiments, the maximum plasma density in a nonuniform plasma may appreciably exceed the background value.     

Local field effects and stimulated multimode scattering of resonance radiation in a two-level medium

Scattering of resonance radiation in a dense two-level medium is considered with allowance for the local field effects. The system is studied in the framework of the mean-field approximation for a modified hierarchy of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices of an ensemble of atoms and modes of a quantized electromagnetic field. The local field correction is consistently derived from the initial Hamiltonian of the system. The problem of scattering of a short rectangular pulse from a quasi-point sample is considered numerically and theoretically. The possibility of a multimode spectrum of scattered radiation with frequencies multiple of the Rabi frequency and with other intermediate frequencies is demonstrated. The relative intensities of spectral lines are determined.     

A dynamics-controlled truncation scheme for the hierarchy of density matrices in semiconductor optics

We discuss the interaction of coherent electromagnetic fields with the semiconductor band edge in a dynamic density matrix model. Due to the influence of the Coulomb-interaction then-point density matrices are coupled in an infinite hierarchy of equations of motion. We show how this hierarchy is related to an expansion of the density matrices in terms of powers of the exciting field. We make use of the above results to set up a closed set of equations of motion involving two-, four-and six-point correlation functions, from which all third order contributions to the polarization can be calculated exactly. Comparison of our treatment of the hierarchy with the widely used RPA decoupling on the two-point level, gives interesting insight into the validity of the RPA. In particular we find, that a RPA-like factorization for two of the relevant density-matrices yields a solution of their respective equations of motion to lowest order in the electric field.     

Enhancement of electron density in the interaction of high-power electromagnetic waves with inhomogeneous magnetized plasma

Propagation characteristics of a high-power electromagnetic wave through an inhomogeneous magnetized plasma is investigated. Considering the momentum transfer equations for electrons and ions and taking into account the ponderomotive force, the distribution of electron density and dielectric permittivity are obtained. Using non-linear dielectric permittivity and Maxwell's equations in the absence of external current and charge densities, non-linear wave equations are achieved. The results indicate that the external static magnetic field can modify the profiles of both the electric and magnetic fields. It is also shown that the external static magnetic field enhances the amplitude of the electron density and the non-linear dielectric permittivity.