Bose-Einstein condensation in a static scalar field from the standpoint of the Goursat problem

The Goursat problem, developed by the present authors in previous papers [Ukr. Fiz. Zh. (Russ. Ed.) 27, 1602 (1982); Differentsial’nye Uravneniya 20, 302 (1984); J. Math. Phys. 33, 233 (1996)], is used to study the energy spectrum of a scalar relativistic particle in a static axisymmetric external scalar field of an attractive nature. This is obviously a model. It is shown that the problem formulated in this way has no unstable solutions, i.e., solutions increasing with time, in contrast to the Cauchy problem, where such solutions appear when the square of the particle frequency (energy) vanishes (in other words, in a Bose-Einstein condensation) Zh. éksp. Teor. Fiz. 112, 1167–1175 (October 1997)     

Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Calculation of the force characteristics of a multi-coil suspension of a superconducting sphere

The theory presented in the accompanying paper [Ref. 1: Zh. Tekh. Fiz. 67(1), 3 (1997); Tech. Phys. 42, 1 (1997)] for the calculation of the magnetic field and the force characteristics of an electromagnetic suspension for a superconducting body is used to carry out specific calculations of the force characteristics of a multi-coil suspension of a superconducting sphere. Formulas are obtained for the dependence of the force and the stiffness, from which it is possible to approach the problem of the stable suspension of a superconducting sphere in the field of a system of circular currents. The problem of determining the magnetic field at the sphere is analyzed and the conditions are found for which it is less than the critical field. Zh. Tekh. Fiz. 67, 10–16 (January 1997)     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

Abstract

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

A DMRG study of the -symmetric Heisenberg chain

The spin one-half Heisenberg chain with U q [ SU (2)] symmetry is studied via density-matrix renormalization. Ground-state energy and q-symmetric correlation functions are calculated for the non-Hermitian case with integer r. This gives bulk and surface exponents for (para)fermionic correlations in the related Ising and Potts models. The case of real q corresponding to a diffusion problem is treated analytically. Received: 18 February 1998 / Accepted: 17 March 1998     

On the critical distance in heavy-ion collisions

An analytical expression is obtained for the electron energy term by solving a two-center Dirac problem. This expression has the correct asymptotic form in two limiting cases — the Popov approximation and the nonrelativistic problem. Zh. Tekh. Fiz. 69, 135–137 (August 1999)     

A Two-Phase Free Boundary Problem for the Nonlinear Heat Equation

Abstract

A two-phase free boundary problem associated with nonlinear heat conduction is considered. The problem is mapped into two one-phase moving boundary problems for the linear heat equation, connected through a constraint on the relative motion of their moving boundaries. Existence and uniqueness of the solution is proved for small times and a particular exact solution is discussed.     

Mathematical Simulation of Heat Transfer in Relaxing Media

Abstract

We find a numerically-analytical solution of a boundary problem for the third-order partial differential equation, which describes the mass and heat transfer in active media.     

Pairing in the Hubbard model: the Cu O cluster versus the Cu-O plane

We study the Cu₅O₄ cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantization. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W =0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W =0 pairs of d symmetry, due to a spin fluctuation, and ssymmetry, due to a charge fluctuation. Flux quantization is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size. Received 23 July 1999     

Global Uniqueness in the Inverse Scattering Problem¶for the Schrödinger Operator¶with External Yang–Mills Potentials

We consider the Schr?dinger equation in R ⁿ , n≥ 3, with external Yang–Mills potentials having compact supports. We prove the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain. A similar uniqueness result holds for the inverse scattering problem at a fixed energy. Received: 11 August 2000 / Accepted: 24 May 2001     

Electronic properties of CuO 2 -planes: A DMFT study

We study one-particle spectra and the electronic band-structure of a CuO ₂ -plane within the three-band Hubbard model. The Dynamical Mean-Field Theory (DMFT) is used to solve the many particle problem. The calculations show that the optical gap is given by excitations from the lower Hubbard band into the so called Zhang-Rice singlet band. The optical gap turns out to be considerably smaller than the bare charge transfer energy () for a typical set of parameters, which is in agreement with experiment. We also investigate the dependence of the shape of the Fermi surface on the different hopping parameters t CuO and t OO. A value t OO / t CuO >0 leads to a Fermi surface surrounding the M point. Received 21 September 1998 and Received in final form 8 June 1999     

Resolving of discrete transformation chains and multisoliton solution of the 3-wave problem

Abstract

The chain of discrete transformation equations is resolved in explicit form. The new found form of solution alow to solve the problem of interrupting of the chain in the most strigtforward way. More other this form of solution give a guess to its generalization on the case of arbitrary semisimple algebra in the case of n-wave problem. This technique is demonstraited on the example of construction multi-soliton solution of the 3-wave problem in explicit form.     

Knudsen Layer for Gas Mixtures

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math. 39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.     

Propagation of a moving point source in a stratified medium with fluid flow

Summary The problem of an acoustic field generated by a point source moving with arbitrary velocity in a stratified medium in still air has been addressed by Limet al. (Lim P. H. andOzard J. M.,J. Acoust. Soc. Am.,95 (1994) 131). The aim of this paper is to investigate the same problem in the presence of a moving fluid.     

Trimmed autocalibrating k-space estimation based on structured matrix completion

PurposeParallel imaging allows the reconstruction of undersampled data from multiple coils. This provides a means to reject and regenerate corrupt data (e.g. from motion artefact). The purpose of this work is to approach this problem using the SAKE parallel imaging method.Theory and methodsParallel imaging methods typically require calibration by fully sampling the center of k-space. This is a challenge in the presence of corrupted data, since the calibration data may be corrupted which leads to an errors-in-variables problem that cannot be solved by least squares or even iteratively reweighted least squares. The SAKE method, based on matrix completion and structured low rank approximation, was modified to detect and trim these errors from the data.ResultsSimulated and actual corrupted datasets were reconstructed with SAKE, the proposed approach and a more standard reconstruction method (based on solving a linear equation) with a data rejection criterion. The proposed approach was found to reduce artefacts considerably in comparison to the other two methods.ConclusionSAKE with data trimming improves on previous methods for reconstructing images from grossly corrupted data.     

Krein Signatures for the Faddeev-Takhtajan Eigenvalue Problem

One of the difficulties in analyzing eigenvalue problems that arise in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider the problem of locating and counting the discrete eigenvalues associated with the Faddeev-Takhtajan eigenvalue problem, for which the sine-Gordon equation is the isospectral flow. In particular we show that for potentials having either zero topological charge or topological charge ± 1, and satisfying certain monotonicity conditions, the point spectrum lies on the unit circle and is simple. Furthermore, we give an exact count of the number of eigenvalues. This result is an analog of that of Klaus and Shaw for the Zakharov-Shabat eigenvalue problem. We also relate our results, as well as those of Klaus and Shaw, to the Krein stability theory for J-unitary matrices. In particular we show that the eigenvalue problem associated to the sine-Gordon equation has a J-unitary structure, and under the above conditions the point eigenvalues have a definite Krein signature, and are thus simple and lie on the unit circle.     

On the Far Infra Red Excitation of LO Vibrations in Thick Single Crystals

New experiments show that the solution of the complicated problem of Far Infrared (FIR) absorption by crystals of very low symmetry, illuminated at quasi-normal incidence, might have a simple solution, which has been suggested now that a number of spectroscopic studies on monoclinic Triglycine Sulphate (TGS) are available: i) in a first classical approximation where only the strongest bands are considered, the absorption spectrum depends only on the direction of the electric field E of the IR radiation, and Transverse Optic (TO) vibrations are directly excited with electric dipole variations dp parallel to E. ii) in a second approximation looking only at the weakest absorption bands, it depends only on the direction of the wave vector k and Longitudinal Optic (LO) vibrations are excited with dp parallel to k and extinction coefficients 3 orders of magnitude smaller.     

Structure of spin polarons in the t-t′ -t″ -Jz model

We calculate the Green function in the t-t '-t ”-J^z model and analyze the deformation of the quantum Néel state in the presence of a moving hole. Solving the problem in a self-consistent Born approximation and using Reiter's wave function we have found various spin correlation functions. We show that the different sign of hopping elements between the hole- and electron-doped system of high- cuprates is responsible for the sharp difference of the polaron structure between the two systems with antiferromagnetism stabilized in the electron-doped case by carriers moving mainly on one sublattice. Received 11 January 2000     

Magnetization of a diffusive ring: Beyond the perturbation theory

Average persistent current over a set of diffusive metallic rings with fixed number of electrons is considered. We study the case in which the phase breaking time is much greater than an inverse average interlevel distance. In such a case, many return events for an electron must be taken into account. As a result, one arrives at a nonperturbative problem for a cooperon mode fixed by an external magnetic field. This multi-cooperon problem has been considered previously by Altland et al., [Europhys. Lett. 20, 155 (1992)] and in several following papers within the framework of supersymmetric approach. Such an approach involves very tedious calculations which were performed using a computer algebraic package. Here we solve the problem in question with the help of a replica trick. It is demonstrated that the replica trick in combination with a proper analytical continuation in the replica space allows one to obtain the result in much more explicit way. Zh. éksp. Teor. Fiz. 111, 1057–1070 (March 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

Abstract

It is shown that for scattering from a plane in an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behaviour. If the angle of incidence is fixed (in general it should not be small), the diffusive component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation, and for the Neumann problem it does not depend on θ. For the backscattering case these dependences correspondingly become θ⁴ and θ°. The result is obtained from the structure of the equations that determine the scattering problem rather than by use of an approximation.