Stochastic linear maps and transition probability

Some aspects of the transition probability P(, ) between states , on unital ^*-algebras are discussed. It is shown that P increases under the action of any stochastic linear map T, i.e., P(T, T)P(, ). Some properties of P are derived in starting from a recently-proved characterization of the quantity in question.     

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.     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

Nonlinear Response of the Semiconductor Laser with Pump Current Modulation

The influence of tuning the lasing monochromatic radiation frequency _g within the amplification band on the nonlinear response of the semiconductor laser with harmonic modulation of pump current is investigated theoretically. It is established that the principal features of the behavior of the nonlinear amplitude-detuning characteristic (ADC) are determined by the relation between the current modulation frequency _m and the main resonance frequency of the laser _r. If _{m r}, then with increase in _g the response decreases monotonically mainly due to the decrease of its dynamic component. The exception is provided by the spectral regions where peaks on the ADC appear because of the explicitly nonlinear lasing regimes (period doubling, chaos, etc.) When _m < _r, the resonance conditions for induced oscillations are satisfied only for definite spectral intervals within the amplification band and a dip appears on the low-frequency side of the ADC. With decreasing _m, the dip boundary shifts to a more high-frequency region of the band corresponding to smaller local resonance frequencies. The peaks on the ADC corresponding to the radiation period doubling shift to the region of smaller values of _g on increase in _m.     

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II

As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of harmonic oscillators, while the other one is any dynamical system ofn degrees of freedom. Such a problem is of interest both for the realization of holonomic constraints of classical mechanics, and for the freezing of the internal degrees of freedom in molecular collisions. The results of Part I, which referred to the particular case =1, are here extended to the more difficult case >1. For the rate of energy transfer we find exponential estimates of Nekhoroshev's type, namely of the form exp (_*/)^1/a , where is a positive real number giving the size of the involved frequencies, and _* anda are constants. For the particularly relevant constanta we find in generala=1/ however, in the particular case when the frequencies are equal (collision of identical molecules), we finda=1 independently of , as conjectured by Jeans in the year 1903.     

A Far IR Study of NbN in the Normal and Superconductive State

A thin film of NbN (thickness t = 300 Å), has been deposited on an MgO and a Si wafer. Both samples have been studied by transmission from 10 or 20 to 120 cm^–1, and have exhibited one maximum of transmission at a given frequency like the classical superconductors as Pb, Sn or Hg in the superconductive state. From the Far IR experimental data, the characteristic temperature _c, and the gap frequency (_gap () = 2 (), () being the energy gap) are immediately obtained (for instance for the NbN / MgO sample, _c = 15.5 K; _g (5 K) = 39.7 cm^–1), and it is seen that as expected from the BCS theory for a weak coupling. To fit the data we had to adjust only two additionnal parameters: collision and plasma frequency, _c () and _p (including all carriers). At = 5 K, thebest fit for the NbN / MgO sample is obtained with _c = 371 cm^–1 and _p = 12,600cm^–1.     

Goldstone theorem for bose systems

In three or more dimensions (3) it is proved that if the correlations decay faster than |x|^-(-20) then gauge symmetry breaking is excluded. In one and two dimensions (=1 or 2) the gauge symmetry is always preserved.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Manifestation of Extracoordination in the Resonance Raman Spectra of Water‐Soluble Cation Co‐Porphyrins

Resonance Raman spectra (RRS) of Co(II) and Co(III)5,10,15,20tetrakis(4Nmethylpyridinium)porphyrin ((Co^II(TmpyP4), and Co^III(TMPyP4)) in aqueous solutions at different pH as well as in organic solvents (methanol, ethanol, DMSO, DMF) are obtained. The increased sensitivity of the oscillation frequencies ₂, ₄, ₈, and ₆ — the markers of the oxidation state of a metal — to the nature of an axial ligand has been revealed. For Co^III(TmpyP4), the shifts of the indicated frequencies in extracoordination have turned out to be twofold larger than those for Co^II(TmpyP4). The spectral effects observed are related to different electron influence of the extraligands on the system of the porphyrin ring. In the case of Co(III)porphyrin, interaction of the d orbitals of the metal and the e _g ^*orbitals of the macrocycle is more efficient since its ionic radius is smaller than for the Co(II)complex. For Co^III(TmpyP4), a linear correlation between the oscillation frequencies ₂, ₄, ₈, and ₆ and the experimental Gutmann parameters characterizing the electronacceptor properties of solvents is found.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Derivation of the Tully—Fisher Law: Doubts About the Necessity and Existence of Halo Dark Matter

For disk galaxies the fourth power of the circular velocity ⁴ _c of stars around thecore of the galaxy is proportional to the luminosity L, ⁴ _c L (Tully—Fisher law).Since L is proportional to the mass M of the galaxy, it follows that ⁴ _c M.Newtonian mechanics, however, yields ² _c = GM/r for a circular motion. In orderto rectify this big difference, astronomers assume the existence of dark matter.We derive the equation of motion of a star moving in the central field of a galaxyand show that, for a circular motion, it yields a term of the form ⁴ _c GMc/,where G is Newton's gravitational constant, c is the speed of light, and is theHubble time. This puts in doubt the existence of halo dark matter for galaxies.     

Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg are conserved under the transformation betweeng and the new metrich . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg when the latter is a solution of theories with a quadratic or polynomial Lagrangian.     

Geometric localization of the threshold in two-dimensional Ising ±J spin glasses forT=0

Following an approach of Toulouse, ground states in random 2D Ising ±J spin glasses (without external magnetic field), on square lattices, and with concentrations 0p0.5 of antiferromagnetic bonds are studied by means of minimal matchings of frustrated plaquettes. Lete(p) be the ground-state energy per spin in the thermodynamic limit. Then the well-known equatione(p)=–2+(p)f(p) holds, wheref(p) is the concentration of frustrated plaquettes and(p) is the average connection length between paired frustrated plaquettes in minimal matchings. Introducing (p) as the probability that a frustrated plaquette is matched to another frustrated plaquette by a connection of length (in a minimal matching), the average length(p) can be rewritten asgl(p)=(p). The study of(p) and its components (p) leads to an intervalp ^*pp ₂ (p ^*0.121±0.008,p ₂0.161±0.008) where the threshold between ferromagnet and paramagnet forT=0 lies. Analyzing a similar so-called adjoined average lengthl(p) admits further insight.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Ising Models on Hyperbolic Graphs II

We consider Ising models with ferromagnetic interactions and zero external magnetic field on the hyperbolic graph (v, f), where v is the number of neighbors of each vertex and f is the number of sides of each face. Let T _c be the critical temperature and T _c =supTT _c: ^f=( ⁺+ ^–)/2, where ^f is the free boundary condition (b.c.) Gibbs state, ⁺ is the plus b.c. Gibbs state and ^– is the minus b.c. Gibbs state. We prove that if the hyperbolic graph is self-dual (i.e., v=f) or if v is sufficiently large (how large depends on f, e.g., v35 suffices for any f3 and v17 suffices for any f17) then 0<T _c <T _c, in contrast with that T _c =T _c for Ising models on the hypercubic lattice Z ^d with d2, a result due to Lebowitz.⁽²²⁾ While whenever T<T _c , ^f=( ⁺+ ^–)/2. The last result is an improvement in comparison with the analogous statement in refs. 28 and 33, in which it was only proved that ^f=( ⁺+ ^–)/2 when TT _c and it remains to show in both papers that ^f =( ⁺+ ^–)/2 whenever T<T _c . Therefore T _c and T _c divide [0, ] into three intervals: [0, T _c ), (T _c , T _c), and (T _c, ] in which ^{+ –} but ^f =( ⁺+ ^–)/2, ^{+ –} and ^f ( ⁺+ ^–)/2, and ⁺= ^–, respectively.     

Three- and five-dimensional considerations of the geometry of Einstein's* g-unified field theory

We study the algebraic and differential geometric structures of three- and five-dimensional^* g-unified field theory, with emphasis on the five-dimensional^* g-unified field theory, in which we derive a new set of powerful recurrence relations which hold in a five-dimensional generalized Riemannian manifoldX ₅ , prove a necessary and sufficient condition for the existence and uniqueness of the solution of the system of the Einstein equations in the first two classes, and find a precise tensorial representation of the Einstein connection in terms of^*g .     

An approximation method to solve Einstein's field equations on a curved background metric

An approximation method is developed to calculate the gravitational field of a matter sourceT moving on a curved background metric that is an exact solution of the field equations and deviates only weakly from flat space-time. The fieldh of the sourceT is supposed to be much smaller than the curved part of the background, so that in the series expansion ofh each order can be expanded in powers of the background.