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.     

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.     

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.     

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.     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.     

On exact allowance for masses,anomalous magnetic moments,and electric dipole moments of the neutrinos in the ν1 → ν1ν2¯ν2 reaction in an external field

The probability of the process _{1 12}¯₂ in the field of a plane wave is calculated in the general case with allowance for masses, anomalous magnetic moments, and electric dipole moments of the neutrinos. In special cases, earlier results are confirmed. The symmetry of the expression for the integrated probability with respect to the anomalous magnetic moment and the electric dipole moment of the neutrinos is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 101–105, January, 1992.     

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.     

The turning of magnetotactic bacteria

A magnetotactic bacterium aligns itself along the magnetic field. When the field is reversed the bacterium makes a U-turn in the surrounding water. The turning is described by a Fokker-Planck equation for the angle , which is singular at the endpoints =0 and =. The time needed for turning can be found exactly as a first-passage time. The probability distribution itself can be found in terms of an approximation for low temperature. To cover the regions near the endpoints singular perturbation theory is needed.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

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.     

Narrowband tunable sub-millimetre hot hole injectionless semiconductor laser and its use for cyclotron resonance investigation

A narrowband far-infrared laser on intersubband transitions of hot holes was constructed and investigated. Two methods were used: mode selection due to intercavity Fabry-Perot resonator and selection of a narrow spectral lasing region by special multilayer mirror. The emission spectra of the laser were determined. The radiation bandwidth measured was 0.2 cm^-1 as compared with 15–30 cm^-1 for nonselective resonator. Lasing with selective resonator could occur at any two wavelengths in the ranges 80–120 and 150–200 m. The wavelength was modified by altering electric and magnetic fields. The radiation power was about 10 W and of the same kind as that of a laser without a mode selector. The narrowband laser was used in investigation of CR of electrons in n-InSb.     

Weakly singular perturbations of a discrete spectrum

We consider weakly singular perturbations ¦x¦^–(0<<2) of an even restoring potential. We compute the matrix elements of the perturbation together with the additional point potential associated with the perturbation. It is shown that even for unperturbed wave functions, the matrix elements exist when 0 < < 3/2. The series for the Rayleigh-Schrödinger coefficients converge in all orders for the same interval in , regardless of the form of the restoring potential. For odd states, the matrix elements of the perturbation exist when 0 < < 3, while estimates for the Rayleigh-Schrödinger coefficients give the boundary = 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 14–18, June, 1989.     

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.     

Higher-order theory of gravitation

The field equations obtained by introducing a correction in the Hubert Lagrangian in the form of a series of finite terms inR (g R ) are considered in order to study the implications for the cosmological singularity.     

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.     

Instability of two counter-streaming gyrating beams of electrons

The linear theory of the two-beam instability of weak gyrating beams is investigated. Maximum growth rates of instabilities, instability limits and frequencies of unstable waves are numerically determined. The aperiodic instability withk _{z z0}= _c( _z0 is the velocity of the beam along the magnetic field, _c is the cyclotron frequency andk _z is the longitudinal wave number) and the instability with= _c/2 and withk _{z z0}= _c/2 possess greatest growth rates. Dependence of growth rates on longitudinal and transversal components of the wave vector is investigated in detail.     

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.     

Singular perturbations of discrete spectrum

Even solutions of the Schrödinger equation with retaining potential x² are constructed for singular perturbation potentials |x|^–. It is shown that the perturbation automatically entails an induced point potential, taking account of which the perturbation matrix elements and Rayleigh-Schrödinger series may be constructed when 1 < < 3/2. In the opposite case (3/2 2), although the solutions are analytic with respect to , not even diverging series can be obtained for the energy solutions without solution of the Schrödinger equation. The analogy with quantum field theory is explored.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 58–64, March, 1988.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).