Faculty of Physics
M.V.Lomonosov Moscow State University

## Invariant operators of inhomogeneous groups. I. The IGL(N,R)group

### A.P. Demichev and N.F. Nelipa

Moscow University Physics Bulletin 1980. 35. N 2. P. 1

It is shown that the algebra of the Lie group of real inhomogeneous general linear transformations IGL(n,R) has no invariant operators.

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## Invariant operators of inhomogeneous groups. II. The ISL (n,R)group

### A.P. Demichev and N.F. Nelipa

Moscow University Physics Bulletin 1980. 35. N 2. P. 6

It is shown that the real inhomogeneous unimodular linear group of arbitrary dimensionality ISL(n,R) has one Casimir operator. An explicit form of the invariant operator is obtained in the case of ISL(2,R).

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## Electron - fhonon interaction in the vicinity of a van-hove singularity

### Yu.P. Drozhzhov

Moscow University Physics Bulletin 1980. 35. N 2. P. 10

The interaction between electrons and acoustic phonons in the vicinity of a Van - Hove singular point is considered. It is shown that even weak interaction leads to a considerable change in the characteristics of the electron gas in the region of the singularity. The electron spectrum changes from quadratic to linear, while the density of states falls off linearly in the neighborhood of the singular point.

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## The possibility of amplitude compensation of thermal self-defocusing of a beam of light (a numerical experiment)

### V.A. Vysloukh, K.D. Egorov and V.P. Kandidov

Moscow University Physics Bulletin 1980. 35. N 2. P. 16

The possibility of suppressing the effects of self - defocusing by a rational choice of the Initial intensity distribution in the beam channel is investigated. Compensation of the defocusing in a fixed and moving medium is considered, and also when scanning the beam. The method of finite elements is used for the calculation.

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## Two problems of nonstationary thermal self-action

### V.A. Vysloukh and S.S. Chesnokov

Moscow University Physics Bulletin 1980. 35. N 2. P. 21

Two nonstationary thermal self-action modes are considered: for pulse durations of the order of the transit time of the acoustic wave through the transverse cross section of the beam and of the order of the time taken for a steady temperature to be established in the beam channel. The method of finite elements is used to solve the quasi-optics equation. The equations of hydrodynamics and nonstationary thermal conduction are solved using the Fourier - Bessel transformation. A number of results of a numerical experiment are given for different values of the parameters of the medium in the beam.

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## The action of Ƴ-radiation on the electrical characteristics of natural quartz

### V.G. Zubov, A.P. Shtyrkova, Т.M. Glushkova and M.M. Firsova

Moscow University Physics Bulletin 1980. 35. N 2. P. 28

The temperature - frequency dependences (20-700°C; 0.5-10 kHz) of the dielectric characteristics (ε and tgδ) of natural quartz crystals irradiated with Ƴ-quanta from $^{60}$Со in the dose range 5x10$^5$—2x10$^9$ Rare investigated. It is shown that the maximum loss and the beginning of the rapid increase in ε are shifted due to the irradiation towards higher temperatures, and the shift is greater the higher the radiation dose. It is found that unlike optical properties the radiation change in ε and tgδ does not reach saturation over the whole dose range. A series of successive annealings of the specimens atincreasing temperatures shifts the peak of tg6 and the beginning of the increase in ε in the opposite direction to the temperature, but even annealing at 720°C does not convert the specimen to its initial state. In analyzing the results the applicability of the model of hole Al-centers (used to describe the change in the optical properties due to the action of radiation) to dielectric relaxation processes is discussed.

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## Stability of the flows of an ideal nonuniform liquid

### D.M. Alishaev

Moscow University Physics Bulletin 1980. 35. N 2. P. 34

The stability of two - dimensional stationary flows of an ideal nonuniform liquid with respect to arbitrary three - dimensional infinitely small perturbations is investigated. The time - asymptotic behavior of the solutions of the hydrodynamic equations linearized with respect to the mean state is examined. It is shown that the flow is conditionally stable when Ri > 1/4 everywhere in the flow (the velocities are limited while the vortex increases linearly), and unstable in the regions where Ri < 1/4 (the perturbation energy increases without limit at the expense of the energy of the main flow).

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## Theory of superradiation in the raman scattering of light

### V.I. Emel'yanov and V.N. Seminogov

Moscow University Physics Bulletin 1980. 35. N 2. P. 40

The process of superradiation (collective spontaneous radiation) in the Raman scattering of an intense electromagnetic wave by an ensemble of molecules is considered. Using the results obtained the mechanism of collisionless excitation of molecules in intense laser fields is discussed.

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## Collinear acousto-optical filtering in quartz

### V.B. Voloshinov, I.V. Nikolaev and V.N. Parygin

Moscow University Physics Bulletin 1980. 35. N 2. P. 46

The collinear acousto - optical filtering of light in crystalline quartz is investigated. It is shown that when the length of the region of interaction between the light and acoustic beams in increased there is a reduction in the passband of the filter. At the same time the rerquirements imposed on the degree of collimation of the beams are inc reased. At a wavelength of the light of λо= 633 nm apassband of Δλ=0,42 nm is achieved.

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## Markovian nonlinear noneqdilibrium thermodynamic relations with external forces

### R.L. Stratonovich and A.V. Tolstopyatenko

Moscow University Physics Bulletin 1980. 35. N 2. P. 51

Исследован вопрос, как по релаксационному уравнению без внешних сил строить релаксационное уравнение с силами. Получены двухиндексные и трехиндексные соответствующие соотношения.

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## The cooling of a gas by a resonant electromagnetic field under saturation conditions

### S.N. Luzgin

Moscow University Physics Bulletin 1980. 35. N 2. P. 59

The cooling of a gas by the field of a standing electromagnetic wave for an arbitrary field amplitude is investigated. In weak fields, when there is no saturation, the rate of cooling is proportional to the incident power, the increase then slows down, and up to the boundary of the region of nonuniform broadening the rate of cooling is proportional to the square root of the radiation power. In the region of uniform broadening(intense field)the increase in the rate of cooling gradually ceases.

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## Collective quantum features of the relaxation of nonlinear polariton excitations

### B.A. Grishanin

Moscow University Physics Bulletin 1980. 35. N 2. P. 63

A closed system of equations of the second - moments approximation for the average values and correlation functions of the atomic operators is obtained neglecting the mutual effect of quantum fluctuations of the populations in different atoms. The nonlinearity in these equations is introduced solely by the populations via the diagonal part of the correlation matrix of the atoms. For the case of a rarefied gas a complete investigation of the dynamics of spontaneous superradiation without a phenomenological simplification of the problem of the geometry of the medium is given, i.e., on the basis of an analysis of the collective matrix of the propagation of the excitation. The complete coherence of the superradiation for small Fresnel numbers is established and the coherence is estimated in the general case; the excitation of a very large number of modes and the presence of stochastic intermode beats due to collective frequency shifts which are different for different modes is explained, the dependence of the intensity on the concentration, which is nonquadratic with deviations from quadratic of <10%, and the delay time of the pulse, are refined.

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## Some optical phenomena of the twilight atmosphere

### A.Kh. Khrgian and N.A. Petrenko

Moscow University Physics Bulletin 1980. 35. N 2. P. 71

The illumination produced in the twilight by the scattering of light in an aerosol layer of the stratosphere is calculated. It is shown that, particularly under conditions of a clean troposphere, this scattering may explain certain color phenomena that occur at sunset. Observation of these phenomena gives information on the aerosol layers of the atmosphere.

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## Spectral characteristics of wave motion in the surface layer of reservoirs

### V.V. Buklanov and A.A. Pivovarov

Moscow University Physics Bulletin 1980. 35. N 2. P. 77

The results of synchronous measurements of the raising of the water surface, and of the vertical and horizontal components of the velocity of motion of the water at two levels in a deep reservoir are discussed. The autospectra of the measured quantities, the spectra of the square of the coherence of the raising of the water surface and of the vertical component of the orbital velocity, and the phase spectral relations between the vertical and horizontal components of the velocity of motion of the water are presented.

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## Quasi-uniform layer in the ocean on the water temperature in the seasonal thermocline

### A.N. Kabbar and A.A. Pivovarov

Moscow University Physics Bulletin 1980. 35. N 2. P. 83

An analytical solution of the problem is given and the numerical calculations of the effect of the motion of the upper boundary of the quasiuni form layer on the formation of the temperature profile of the water in the seasonal thermocline for different intensities of the turbulent exchange in it are analyzed. The motion of the boundary and the temperature in it are a pproximated by linear functions of time. It is shown that the hypotheses of "freezing" and "self - similarity" of the seasonal thermocline correspond very closely to reality for small turbulent -exchange intensities.

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## The necessary conditions for a regular minimum of the scale factor of comoving space

### V.G. Agakov

Moscow University Physics Bulletin 1980. 35. N 2. P. 90

The necessary conditions for a regular minimum of the scale factor of a frame of reference of a comoving barotropic medium, free from energy flows are refined.

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## An experimental investigation of the disturbances propagating in front of an intense shock wave in xenon

### A.P. Ryazin and Belkasem Ferkhat (Algeria)

Moscow University Physics Bulletin 1980. 35. N 2. P. 95

An experimental investigation is made using an interferometric method of the state of xenon in front of a shock wave propagating in a channel of square cross section in the range of Mach numbers M = 10-25 for initial pressures of 10, 25, and 34.5 mm Hg. It is established that the prefrontal zone is disturbed mainly in the region of the walls of the shock tube. The disturbance is in the form of a sudden change in compression.

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## Electron-phonon interaction in the neighborhood of a Van Hove singularity (II)

### Yu.P. Drozhzhov

Moscow University Physics Bulletin 1980. 35. N 2. P. 98

The interaction between phonons and electrons close to a Van Hove singular point of the S$_2$ type is considered using methods not based on perturbation theory. It is shown that weak interaction considerably changes the spectrum and density of states in the region of the singularity.

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## The shape of the hanle signal in crossed beams

### A.L. Kotkin, V.V. Maiorshin and R.M. Umarkhodzhaev

Moscow University Physics Bulletin 1980. 35. N 2. P. 103

The shape of the Hanle signals in crossed beams as a function of the spectral composition and polarization of the interrogation beam is investigated experimentally. The shape of the observed signals can be explained by the presence of nonresonant light in the interrogation beam.

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## Control of the polarization of the emission of a solid-state Nd:YAG laser

### V.N. Parygin, A.I. Portnyagin and S.К. Рак

Moscow University Physics Bulletin 1980. 35. N 2. P. 106

The possibility of controlling the polarization characteristics of the emission of a YAG laser is investigated. A crystal of LiNbO$_3$ is placed in the resonator and a voltage is applied to it. Experiment shows that the plane of polarization of the radiation can be rotated by changing the electric signal applied to the electrooptical crystal.

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## Estimate of the conditions for the occurrence and the frequency of current oscillations at a virtual cathode

### Yu.K. Alekseev and A.I. Kostienko

Moscow University Physics Bulletin 1980. 35. N 2. P. 109

A modified diode with a constant resistance in the collector circuit is considered. The conditions for oscillations to occur at the virtual cathode are analyzed. An expression is obtained for the oscillation frequency by means of which one can calculate the upper frequency limit for some practical cases. An experiment to observe oscillation at the virtual cathode is described.

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## A method of measuring the dielectric constant of solid slightly absorbing materials using an open resonator

### Yu.K. Alekseev and A.I. Kostienko

Moscow University Physics Bulletin 1980. 35. N 2. P. 113

A simple method of measuring the dielectric constant of slightly absorbing sheet dielectrics using an open resonator in the millimeter wave band is proposed. Measurements of the dielectric constant of a number of specimens were carried out both using the proposed method and a wellknown waveguide method. The results are in good agreement within the limits of experimental error.

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## The mechanism of the storage effect when measuring the surface conductivity of germanium in transverse electric fields

### R.V. Prudnikov and V.A. Matveev

Moscow University Physics Bulletin 1980. 35. N 2. P. 116

The mechanism of the storage effect in an atmosphere of Н$_2$О and NH$_3$ vapor in specimens of n - type germanium is investigated. It is shown that the storage effect arises in Н$_2$О vapor and is not present in NH$_3$ vapor and depends to a large extent on what sort of carriers are concentrated in the germanium surface. A new "proton" mechanism of the storage effect is proposed.

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## Effect of amorphization on the elastic properties of crystalline quartz irradiated with fast neutrons

### L.P. Osipova and Yu. A. Ivashkin

Moscow University Physics Bulletin 1980. 35. N 2. P. 119

It is shown that the change in the elastic moduli S$_{11}$, S$_{13}$, S$_{14}$, S$_{33}$ and S$_{44}$ of crystalline quartz irradiated with fast neutrons can be satisfactorily explained using a model which takes into account the reduct ion in the crystal phase due to an increase in the fraction of the amorphous phase, effective heating of the crystal matrix, and the action of negative stresses proportional to the content of the amorphous phase.

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