Exact solution of general-relativity equations for vibratory collapse

In our previous article (cited as [A]) general requirements were formulated for the solutions of the general-relativity equations that follow from the geometry in the large and from the requirement that the origin be physically realizable [1]. In this article an exact self-consistent equation is described that takes full account of these requirements. The self-consistency is constant with respect to the volume density in the case of a dustlike ball [A17]. Although the self-consistent solution is of measure zero, it enables one to judge the properties of a wide class of solutions as shown by the experience of hydrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 90–98, July, 1977.     

Schrödinger operators with symmetries

We consider the stationary Schrödinger operator H of a many-body system M with two-body rotation invariant interactions. The operator H is reduced with respect to the symmetries of permutation of identical particles, rotations and reflections, into a direct sum of operators H^τ̃, where τ̃ is an index of the irreducible representations of the symmetry group of the system.The spectra of the operators H^τ̃ were investigated in a series of papers of G.M. Zislin and A.G. Sigalov ([20], [21], [31]-[35]). In a recent paper [3] we have developed the spectral theory of these operators on the basis of the Weinberg equations.In the present work we complete and simplify this theory. In particular we treat in detail the case where the given system can be decomposed into two identical subsystems. For such systems there is a certain coupling between permutation and rotation-reflection symmetries, because a permutation, which interchanges the two subsystems, imposes a reflection on the relative position vector of the two centers of mass. This requires a modification of the theorem on essential spectrum as formulated in [3] in the case where such a division is not possible. The importance of this special case, as exemplified by diatomic molecules, fully justifies such a detailed treatment.This special case was treated by Zislin [34] under the assumption that the interactions are essentially multiplicative, relatively compact two-body interactions. Our method allows for general relatively compact two-body interactions, and can without difficulty be generalized to many-body interactions.Moreover, the method based on the Weinberg equation is suitable for a further analysis of the spectra of these operators.     

InGaAs/GaAs应变异质结中的反常离子沟道效应

用5.8,3.0和1.2MeV的Li离子对用MBE制备的In_0.25Ga_0.75As/GaAs(100)异质结在(100)面中沿[100]及[110]轴进行角扫描。5.8MeV时,[110]轴外延层与衬底沟道对准角的差值为0.90°,从而计算出其晶格失配度为1.62％。3.0MeV时,背散射角扫描谱出现了严重的不对称现象。若离子以1.2MeV入射,沟道对准角的差值及衬底沟道的半角宽大大地偏离实际值。本文对以上反常现象从物理机理上进行了分析,给出了这些反常离子沟道 关键词：     

Free Massive Fermions¶Inside the Quantum Discrete sine-Gordon Model

We extend the notion of space shifts introduced in [FV3] for certain quantum light cone lattice equations of sine-Gordon type at root of unity (e.g. [FV1,FV2,BKP,BBR]). As a result, we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation, which is obtained by exponentiating these roots, is exactly the evolution equation for the?“classical background” as described in [BBR]. As an application for the introduced constructions, we derive a one to one correspondence between a special case of the quantum light cone lattice equations of sine-Gordon type and free massive fermions on a lattice, as a special case of the lattice Thirring model constructed in [DV]. Received: 2 December 1996 / Accepted: 19 January 1999     

Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors

We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Friedrich [Math. Nachr. 97 (1980) 117–146] and Hijazi [Math. Phys. 104 (1986) 151–162; J. Geom. Phys. 16 (1995) 27–38]. The special solutions of the Einstein–Dirac equation constructed recently by Friedrich/Kim are examples for the limiting case of these inequalities. The discussion of the limiting case of these estimates yields two new field equations generalizing the Killing equation as well as the weak Killing equation for spinor fields. Finally, we discuss the two-and three-dimensional case in more detail.     

ON GEODESIC COMPLETENESS OF NONDEGENERATE SUBMANIFOLDS IN SEMI-EUCLIDEAN SPACES

In this paper, we study the geodesic completeness of nondegenerate submanifolds in semi-Euclidean spaces by extending the study of Beem and Ehrlich [1] to semi-Euclidean spaces. From the physical point of view, this extend may have a significance that a semi-Euclidean space contains more variety of Lorentzian submanifolds rather than those of Lorentzian hypersurfaces in a Minkowski space as in [1]. From mathematical point of view, since there is no distinction in the analysis of geodesic completeness of Lorentzian submanifolds and nondegenerate submanifolds in a semi-Euclidean space, we treat the mathematically more general case of nondegenerate submanifolds in a semi-Euclidean space. The new ideas leading to this generalization are the sufficient conditions for algorithms in the proofs of the results in [1]. Indeed these sufficient conditions for the algorithms also work well for the nondegenerate submanifolds in a semi-Euclidean space.     

Measuring the 9-component magnetic permeability tensor of ferrites

The magnetic permeability tensor of ferrite monocrystals can, in the general case, be represented as consisting of nine components [1]. In [2] the 6-component magnetic permeability tensor was obtained for a triaxial ferrite monocrystal with low magnetic anisotropy energy magnetized by a constant field in the crystallographic plane (110). In the general case of magnetization in an arbitrary crystallographic direction the tensor becomes a 9-component tensor [3]. In the context of the increasing application of ferrite monocrystals in microwave engineering the question of measuring such a tensor is of current scientific and practical interest. In the present article we propose a method for measuring the 9-component tensor for ferrite materials at microwave frequencies.     

Bistable behaviour in squeezed vacua: I. Stationary analysis

A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected simple closed curves depending on the cooperation parameter [0pt] : is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on [0pt] . We also present results which demonstrate more complicated switching behaviour in the dispersive case. Received 12 March 1999 and Received in final form 20 August 1999     

Theory of Cosmical Coherent Avalanche Catastrophes

Abstract

Recently pulses of the electromagnetic cosmic radiation of varies frequency ranges were detected by means of space flight equipment [1]. But so far the physical nature of the sources of these pulses are not well known. Since the generators of these pulses are at far distances obviously, the latters should have considerable power. But in this case we are forced to accepte that that the radiation is generated not only by the surface but also by the bulk mass of the distant object. It is also reasonable to propose that the objects are superdense ones [2]. In the Latter case the electromagnetic radiation cann't difused up to the surface of a superdense object from the centre and so no electromagnetic and acoustic processes can give radiation from the bulk mass of an object. On the contrary gravitational and neutrino radiation may be generated by the bulk mass of a massive object and at the surface of these objects these radiations tightly bounded to matter may be partly transformed into electromagnetic radiation [3]. And we can suppose that namely this very small part of the whole radiational energy is at time registrated at the earth and space laboratories. The mauy ask why all of the remaining purt of teh rediated energy has not been detected yet? There where made some attempts to performe neutrino astronony equipment out no solar neuttinos have been detected yet. As to the camical gravitational radiation it is pregently inveutigated only at low frequencles and no distinet conclucion about its occurence in been reached in the lilorature.     

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six [1–3] and eight quark interactions [4] is applied to study temperature effects [5] (SU(3) flavor limit, massless case), and [6] (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [7]. The mesonic spectra built on the spontaneously broken vacuum induced by the’ t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.     

Statistical estimate of the deformation of a light pulse in the location of plane stratified clouds

The study of clouds in the lower atmosphere by means of laser location (lidar) started in the second half of the sixties. The first investigations in this direction by Ligda [1] and Collis [2–5] indicated the extensive prospects of optical probe systems in studying the structure and dynamics of clouds. The powerful lasers used in these systems (lasers with pulses as short as 10^–9 sec) help in identifying the upper and lower boundaries and the spatial inhomogeneity of clouds of fairly low density with the resolution necessary for projector probing. As in the case of radar, methods of studying atmospheric objects with lidars are based on an analysis of the information included in the reflected signal. The reflected signal in these cases is formed by the back-scattering of light on diffuse interaction with atmospheric inhomogeneities. The different meteorological nature (shower, fog, haze, etc.) and internal structure of the inhomogeneities reflect differently on the parameters of the signal. In general the intensity, the state of polarization, the shape of the envelope of the pulse, and the energy and frequency spectrum all vary. However, the extraction and analysis of the information contained in these changes in order to solve the inverse problem present an extremely complicated problem, as yet only solved in individual simple cases. In problems relating to the laser probing of clouds and mists, one of the most informative and easily-analyzed characteristics is the degree of deformation of the initial pulse by reason of the repeated scattering of photons. A number of preliminary estimates establishing a relationship between the parameters of the cloud layer and the shape of the reflected light pulse were presented in [6–9]. In [6, 9], in particular, the authors estimated the time characteristics of a diffusely-reflected light signal by the method of statistical tests [10], which is particularly suitable for solving multidimensional problems of atmospheric optics [11]. The algorithm of the Monte Carlo method proposed in [6, 9] and used in the present investigation enables us to allow for the complicated boundary conditions arising in the propagation of a divergent, spatially-limited light beam in a layer-like inhomogeneous scattering medium, and also the transient nature of the process.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–53, February, 1973.     

Van der Waals interaction between flux lines in high- superconductors

In anisotropic or layered superconductors thermal fluctuations as well as impurities induce a van der Waals (vdW) attraction between flux lines, as has recently been shown by Blatter and Geshkenbein in the thermal case [#!BlatterGeshkenbein!#] and by Mukherji and Nattermann in the disorder dominated case [#!NattermannMukherji!#]. This attraction together with the entropic or disorder induced repulsion has interesting consequences for the low field phase diagram. We present two derivations of the vdW attraction, one of which is based on an intuitive picture, the other one following from a systematic expansion of the free energy of two interacting flux lines. Both the thermal and the disorder dominated case are considered. In the thermal case in the absence of disorder, we use scaling arguments as well as a functional renormalization of the vortex-vortex interaction energy to calculate the effective Gibbs free energy on the scale of the mean flux line distance. We discuss the resulting low field phase diagram and make quantitative predictions for pure BiSCCO (Bi₂Sr₂CaCu₂O₈). In the case with impurities, the Gibbs free energy is calculated on the basis of scaling arguments, allowing for a semi-quantitative discussion of the low-field, low-temperature phase diagram in the presence of impurities. Received: 9 February 1998 / Accepted: 17 April 1998     

Long-lived excited states at surfaces: Cs/Cu(111) and Cs/Cu(100) systems

One-electron and multielectron contributions to the decay of transient states in the Cs/Cu(111) and (100) systems are studied by a joined wave-packet propagation and many-body metal response approach. The long lifetime of these states is due to the Cu L and X band gaps which reduce the electron tunneling between Cs and Cu. In the (111) case, the decay is mainly by inelastic e-e interaction, whereas in the (100) case, electron tunneling is dominating. This accounts very well for the experimental findings [Bauer et al., Phys. Rev. B 55, 10 040 (1997) and Ogawa et al., Phys. Rev. Lett. 82, 1931 (1999)].     

Quadrupole test particle as a detector of gravitational waves

In this paper it is shown that in general relativity the theory of motion of quadrupole test particles (QTP's) can be used to describe the energy and angular momentum absorption by detectors of gravitational waves. By specifying the form of the quadrupole moment tensor Taub's [7] equations of motion of QTP's are simplified. In these equations the terms describing the change of the mass and of the angular momentum of a QTP due to external gravitational waves are found to occur. The limiting case of the flat space-time is also briefly discussed.     

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.     

Conformal Orbifold Theories and Braided Crossed G-Categories

The Berezin-Toeplitz deformation quantization of an abelian variety is explicitly computed by the use of Theta-functions. An SL(2n,)-equivariant complex structure dependent equivalence E between the constant Moyal-Weyl product and this family of deformations is given. This equivalence is seen to be convergent on the dense subspace spanned by the pure phase functions. The Toeplitz operators associated to the equivalence E applied to a pure phase function produces a covariant constant section of the endomorphism bundle of the vector bundle of Theta-functions (for each level) over the moduli space of abelian varieties.Applying this to any holonomy function on the symplectic torus one obtains as the moduli space of U(1)-connections on a surface, we provide an explicit geometric construction of the abelian TQFT-operator associated to a simple closed curve on the surface. Using these TQFT-operators we prove an analog of asymptotic faithfulness (see [A1]) in this abelian case. Namely that the intersection of the kernels for the quantum representations is the Toreilli subgroup in this abelian case.Furthermore, we relate this construction to the deformation quantization of the moduli spaces of flat connections constructed in [AMR1] and [AMR2]. In particular we prove that this topologically defined *-product in this abelian case is the Moyal-Weyl product. Finally we combine all of this to give a geometric construction of the abelian TQFT operator associated to any link in the cylinder over the surface and we show the glueing axiom for these operators.This research was conducted in part for the Clay Mathematics Institute at University of California, Berkeley.This work was supported by MaPhySto – A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation     

Field screening kinetics in insulating crystals

A number of studies has been recently performed on MDSDM (metal-dielectric-semiconductor-dielectric-metal) structures, used for radiation modulation [1], efficiency enhancement of luminescent devices [2], and other purposes. In view of the promise of field modulation methods of the nonequilibrium carrier concentration, the study of processes occurring in insulating crystals under a voltage is of considerable practical interest. The charge carrier distribution at constant applied voltage was studied in [3] for the equilibrium case. In this paper we consider field screening kinetics in MDSDM structures for a linearly growing external voltage. It is interesting to consider triangular pulses, since in this case the quasistationary screening regime may be achieved [4, 5]. In particular, optimal conditions for the existence of a polarization cooling effect^* can be realized precisely in this case. The results obtained can serve as a basis for studying more complicated pulses.Translated from Izvestiya Vysshikh Uchebnykh Zavedemi, Fizika, No. 6, pp. 101–105, June, 1972.In conclusion the authors are grateful to V. B. Sandomirskii for his interest in this work and for discussing its results.     

Zum Beugungswirkungsgrad von Volumenhologrammen. Teil II. Reflexionshologramme

In this paper we give an exact solution of the coupled differential equation system as developed by Kogelnik [1] for the case of symmetrical recording without neglecting the second differentials for the reflection volume hologram. This solution is applicable to dielectric, absorption and so-called mixed volume holograms. There are some remarkable distinctions between our results and those got by Kogelnik for the case of absorption and mixed holograms. It is shown, that under special assumptions and approximations or for special combinations of the material parameters we get the same relations as Kogelnik.