Conditional stability of multiple-charged solitons

The stability of the three-dimensional multiple-charged soliton solutions to the nonlinear field equations is studied by Lyapunov's method. It is proved that an absolutely stable soliton solution can not exist in any field model. By imposing the subsidiary condition ^pQ_i=0 (fixation of charges) we find a sufficient condition for stability of the stationary soliton which includes the inequality ^{k i} (Q ⁱ / ^k <0. An illustrative example is considered.     

Dark Energy and Global Rotation of the Universe

We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory _r,0 can be identified with ^,0 (only dust fluid is admissible) and rotation can exist with _r,0 =^,0 0. However, the best-fit flat model is the model without rotation, i.e., ^,0 =0. In the considered case we obtain the limit for ^,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are _m,0 ~ 0.3, _r,0 ~ 10^-4, then the SN Ia data show that ^,0 -0.01 (or ₀ > 2.6 · 10^-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is _r,0 ( - 0.01, 0.04).     

Combinations of Observables

This article begins with a review of the framework of fuzzy probability theory.The basic structure is given by the -effect algebra of effects (fuzzy events) E(,A) and the set of probability measures M ⁺ ₁ (, A) on a measurable space (,A). An observable X: B E(, A) is defined, where (, B) is the value spaceof X. It is noted that there exists a one-to-one correspondence between states onE(, A) and elements of M ⁺ (, A) and between observables X: B E(,A) and -morphisms from E(, B) to E(, A). Various combinations ofobservables are discussed. These include compositions, products, direct products,and mixtures. Fuzzy stochastic processes are introduced and an application toquantum dynamics is considered. Quantum effects are characterized from amonga more general class of effects. An alternative definition of a statistical map T:M ⁺ ₁ (, A) M ⁺ ₁ (, B) is given.     

Fluctuations of intensity and arrival angles for light waves in spatially-limited collimated beams in a turbulent atmosphere

This paper presents results of an experimental investigation of fluctuations of intensity and arrival angle as a function of the parameter = ka²/L (where k = 2 /,a is the beam radius, and L is the length of the track) for tracks of different lengths. It is shown that, depending on the value of ₀ ² = 1.23 C _n ² k^7/6 L^11/6, the intensity fluctuations can both increase, and also decrease with increase of . The fluctuations of arrival angle have a maximum for beams for which the parameter 5.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 108–112, September, 1973.     

Quantum Ergodicity of Boundary Values of Eigenfunctions

Suppose that ⁿ is a bounded, piecewise smooth domain. We prove that the boundary values (Cauchy data) of eigenfunctions of the Laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle B^*() is ergodic. Our proof is based on the classical observation that the boundary values of an interior eigenfunction , =² is an eigenfunction of an operator F_h on the boundary of with h=^–1. In the case of the Neumann boundary condition, F_h is the boundary integral operator induced by the double layer potential. We show that F_h is a semiclassical Fourier integral operator quantizing the billiard map plus a small remainder; the quantum dynamics defined by F_h can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of Zelditch-Zworski (1996). Novelties include the facts that F_h is not unitary and (consequently) the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions. Ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by S. Ozawa (1993), and was almost simultaneously proved by Gerard-Leichtnam (1993) in the case of convex C^1,1 domains (with continuous tangent planes) and with Dirichlet boundary conditions. Our methods seem to be quite different. Motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form.The first author was partially supported by an Australian Research Council Fellowship.The second author was partially supported by NSF grant #DMS-0071358 and DMS-0302518.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

Anomaly of the soft-mode damping function near phase-transition points due to interaction with acoustic phonons

An expression is derived for the anomalous part (T, ) of the soft-mode damping function due to third-order interaction between critical optical phonons and acoustic phonons. It is shown that in crystals with a large elastic viscosity the damping function of critical phonons can have stronger temperature anomalies near phase-transition points. The frequency dispersion of () is investigated; it is found that the damping is a maximum at =_o for the soft-mode vibrational dynamics and at =0 for the relaxational dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–49, March, 1982.     

Betatron-synchrotron resonance in free electron laser

In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of _s=(p q)2K, p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of _s=2k, but in that of _s=k. The width of region of _s=k is proportional to with (k _w ² /k) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case.     

LETTER: On the Minimal Angular Size in Open, ΛCDM, and Scalar Field Cosmologies

We propose a simple method for determining the redshift z _m at which the angular size of an extragalactic source with fixed proper diameter takes its minimal value. A closed analytical expression, which is often convenient for numerical evaluation is derived. The method is exemplified with the following FRW type expanding universes: the open matter dominated models ( = 0), a critical density model with cosmological constant ( 0), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed.     

Cosmological Relativity: Determining the Universe by the Cosmological Redshift as Infinite and Curved

Using cosmological relativity theory, we derive the formula for the cosmological redshift written explicitly in terms of 1 – , where = /_c is the ratio of the average mass density to the critical closure density. Based on the present day data of observed redshifts, we conclude that < 1, which means the universe is infinite and curved, and expands forever.     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

On the second eigenfunctions of the Laplacian in R2

A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain by intersecting with the boundary of transversely, where is a bounded convex domain ofR ². We prove this conjecture provided has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided is a bounded convex domain ofR ².Supported in part by NSF DMS 84-09447Home Institution: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Results from the First Year of Observations with the Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe (WMAP) has produced all-sky maps in five frequency bands between 23 and 94 GHz that can be used to study the CMB. We present an overview of the results from an analysis of maps made with one year of data. The highlights are that a) the flat CDM model fits the data remarkably well, an Einstein-deSitter model (_tot = 1, =0) does not; b) from the polarization of the CMB there is evidence of the birth of the first generation of stars at z _r 20; c) when the WMAP data are combined and compared with other cosmological probes a cosmic consistency emerges: multiple different lines of inquiry lead to the same results. The best-fit flat cosmological model to just the WMAP CMB data shows that the matter density is _m h ² = 0.14 _–0.02 ^+0.02, the baryon density is _b h ² = 0.024 ± 0.001, and n _s = 0.99 ± 0.04. WMAP continues to operate, and so results will improve.     

Relations between Black Hole Spin and Angular Velocity of Accreting Particles near the Horizon

Evolution characters of angular velocity _H of a Kerr black hole (BH) and distribution characters of angular velocity _p of accreting particles near the BH horizon are investigated in the case of thin and thick disks, respectively. It is shown that _H evolves in a non-monotonous way in the case of thin-disk-pure-accretion, attaining a maximum at a _* 0.994. This evolution character turns out to depend on the radial gradient of _p near the BH horizon. It is proved that both quantities, ( d_H /dt) _ms and ( _p /r)_{r=r H}, vanish at the same value of a _*: a _*0.994, and an explanation for the non-monotonousness of _H is provided.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

The quasilinear theory of two-stream cyclotron instability of electron beams

The paper is devoted to a study of cyclotron instability ( _e) of two opposite beams of electrons from the aspect of the quasilinear effects. For this case of instability the authors evolve the diffusion equation in the velocity space for an averaged distribution function. They estimate the relaxation times , _z of the spreading of the distribution function in the velocity space. At the end of the paper, they compare their results with an experiment described by M. Seidl and P. unka [Phys. Letters11 (1964), 31].     

Half-Sided Translations and tye Type of von Neumann Algebras

Let M be a von Neumann algebra acting on a Hilbert space H and H a cyclic and separating vector for M. If there exists a half-sided translation for M, i.e. a continuous unitary group U(t) with U(t)=, a non-negative spectrum fulfilling Ad U(t)M M for t 0 (or 0), then we will show that either M is of type III₁ or U(t) is trivial.     

β Decay of the Ω− hyperon

The decay of the ^– hyperon (^– Y⁰ + l^– + ) is studied with the polarization of the resulting particles taken into account. The decay probabilities are calculated along with the energy spectra, the degree of longitudinal polarization, and the coefficient of spin correlation between the electron and the (created) hyperon. The spin correlation coefficient arid the longitudinal polarization of the hyperon depend strongly upon the ratio of both vector and axial form factors.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.