Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

The unitary bogoliubov transformation for a quantized scalar field in a friedman space-time

The time-dependent creation and annihilation operators for a complex scalar field, in a Friedmann space-time, defining particle states with respect to which the Hamiltonian is diagonal, are related by a Bogoliubov transformation to the creation and annihilation operators defined in strict analogy with the procedure carried out in Minkowski space. The Bogoliubov transformation is here written in terms of a unitary operator,U, and an expression for that operator is found via the generating functionF=i InU. The properties of the representation obtained by makingU act upon the state vector , to give a new state _U, are discussed. It is shown that the particle-number operator remains constant in such a picture so that the evolution of the system with time is clearly seen to depend upon the energy _k on the one hand, and upon the state vector _U on the other. Also, it is pointed out that this new representation permits the in and out states to be defined unambiguously.On leave of absence from Istituto de Fisica G. Galilei (Padova) and Istituto Nazionale di Fisica Nucleare (Sezione di Padova).     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Fine Structures of the Permittivity and Characteristic Losses of Electrons in Fluorite

Experimental-computational spectra of the permittivity and characteristic losses –Im^–1 for energies in the range 5–21 eV at a temperature of 4.2 K and theoretical spectra of and –Im^–1 of a fluorite crystal are resolved into elementary transition bands. The parameters of transition bands (energies of their maxima E _i, band halfwidths H _i and areas S _i, and oscillator forces f _i) are determined. A correlation of the spectral bands of and –Im^–1is established, and their specific features are elucidated.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

Structural stability properties of friedman cosmology

A dynamical system with Robertson-Walker symmetries and the equation of the statep=, 01, considered both as a conservative and nonconservative system, is studied with respect to its structural stability properties. Different cases are shown and analyzed on the phase space (x=R ^D , y=x).     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Ions trapped near the free surface of superfluid helium: A review

Suitable ions or other charged particles can be trapped electrostatically just below the free surface of superfluid⁴He. Examples of such particles are the socalled negative ion, which is an electron in a bubble, and the so-called positive ion, which is a⁴He⁺ ion surrounded by a small region (snowball) of solid helium. The trapping mechanism can be used to create two-dimensional pools of ions. Three types of experiment can be carried out with such pools: those that relate to the ionic structure; those in which the ions are used as probes of the properties of the superfluid helium; and those in which the pools are studied as examples of simple two-dimensional fluids or solids. Experiments that have been carried out so far are reviewed, and prospects for the future are assessed.     

Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

How to measure the magnetic moment of the tau lepton

We present a method for obtaining bounds on the magnetic moment of the lepton. In order to do this, we study the radiative decayW as a function of the anomalous magnetic moment of the ,a . One can obtain bounds as good asa < 4.05×10^–2, 2.25×10^–2, 4.5×10^–3, and 2.5×10^–3 at the present Fermilab, future Fermilab, SSC, and LHC, respectively.     

Existence of three phases for aP(ϕ)2 model of quantum field

In the two-dimensional model of the quantum field theory with lagrangean density :()²–(–)^{21/2 4}–⁶: there exist (at least) three different phases for small and some ().     

Self-gravitating three-dimensional solitons in nonlinear scale-invariant electrodynamics

A scale-invariant nonlinear modification of Maxwellian electrodynamics within general relativity is proposed. The starting point is the Mie model and its scale-invariant generalization in flat space-timeE ₄. We prove that all static, spherically symmetrical regular field configurations in this new theory, as well as those in the Mie model, possess negative energy. In search of solitonlike solutions with positive masses, we take into account their proper gravitational fields. We show first that in Riemannian space any gauge-invariant electrodynamic theory does not admit regular solutions. Supposing the gauge invariance to be broken inside the particle, we prove the existence of static particlelike solutions with spherical symmetry and positive energy in the scale-invariant electrodynamics described by a Lagrangian density of the form =-Y(I)R/(2)-W(I)F F _u/2+2X(I)R A A , withY, W, andX arbitrary functions of the invariantI=A A . The correspondence with the Maxwellian theory is required.     

Spectral duality for planar billiards

For a bounded open domain with connected complement inR ² and piecewise smooth boundary, we consider the Dirichlet Laplacian- on and the S-matrix on the complement ^c . We show that the on-shell S-matricesS _k have eigenvalues converging to 1 askk ₀ exactly when-- has an eigenvalue at energyk ₀ ² . This includes multiplicities, and proves a weak form of transparency atk=k ₀. We also show that stronger forms of transparency, such asS _{k 0} having an eigenvalue 1 are not expected to hold in general.     

Five-dimensional null-cone structure of big bang singularity

Firedmann model of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five dimensional Minkowski spaceM ⁵ is globally rigid: if F() and F() are isometric imbeddings inM ⁵ there is a motion of M⁵ such that F= °f. The big bang singularity is the vertex of a null half-cone inM ⁵. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Exact distribution of cluster size and perimeter for two-dimensional percolation

Exact series expansion data of Sykes et al. are used to calculate the average numberc _n and perimeters _n of clusters of sizen20 in the site percolation problem for the triangular, square, and honeycomb lattice. At the percolation thresholdp _n we find a sharply peaked distribution of perimeterss _n with mean s _n =((1–p _n )/p _c )n+O(n ) and width s _n ² –S _n ²n ^1.6 where1/=0.39. This perimeter s _n should not be interpreted as a cluster surface in the usual sense. Two tests confirm the universality hypothesis with reasonable accuracy. The asymptotic decay of the cluster numbersc _n withn is consistent with the postulated asymmetry aboutp _c : logc _n –n forn with1 forp<p _c and1/2 forp>p _c .     

The physical properties of linear and action-angle coordinates in classical and quantum mechanics

The quantum harmonic oscillator is described in terms of two basic sets of coordinates: linear coordinates x, p_x and angular coordinates eⁱ, P (action-angle variables). The angular coordinate eⁱ is assumed unitary, the conjugate momentum p is assumed Hermitian, and eⁱ and p are assumed to be a canonical pair. Two transformations are defined connecting the angular coordinates to the linear coordinates. It is found that x, p_x can be physical, i.e., Hermitian and canonical, only under constraints on the p eigenvalue spectrum. The conclusion is that eⁱ can be a unitary operator. A parallel analysis of the classical harmonic oscillator is done with equivalent results.     

Microscopic selection principle for a diffusion-reaction equation

We consider a model of stochastically interacting particles on , where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V() then satisfies ^–1/2V() as. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor ^1/2 and letting. This density solves the reaction-diffusion equation , and under Heaviside initial data converges to a traveling wave moving at the same rate .