On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

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 ().     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Electrical and optical properties and stabilization of the Fermi level in GaP crystals irradiated by electrons and H+ ions

Electrical and optical properties and Fermi level stabilization are studied in GaP crystals irradiated by electrons (E2.2 MeV, D1·10¹⁹ cm^–2) and H⁺ ions (E5 MeV, D1.7·10¹⁶ cm^–2). It is shown that the limiting position of the Fermi level (F_limE_G/2±0.2 eV) is independent of the initial GaP parameters and the type of bombarding particle, but is determined by the condition of local neutrality of the defective GaP. Resistivity values for the irradiated specimens of _max(D)1·10¹³ ·cm were obtained at 300 K. At maximum integral particle fluxes a decrease in crystal resistivity to (3–6)·10⁹ ·cm was observed. The readjustment of GaP absorption spectra in the region hvE_G upon irradiation is related to recharging of gap states by radiation defects upon motion of the Fermi level toward F_lim.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 37–42, December, 1994.     

Contribution to the thermodynamics of the isomorphous γ ⇆ α-transition in metallic cerium

Using the method of the theory of thermodynamic stability and the form of the lines of the phase equilibrium of the isomorphous -transition in metallic cerium, the authors investigate the behavior of the basic thermodynamic characteristics of this transition in the two-phase region and in a neighborhood of the critical point. Attention is focused primarily on the little-studied adiabatic quantities (T/C_V, (–P/V)_S, (T/V)_S). It is shown that along the phase tie-lines these quantities do not depend on V and S; in the limit of the critical point all adiabatic quantities have nonzero minima, and all isodynamic quantities (T/Cp, (–P/V)_T, (T/V)_P) approach zero according to the same law. The obtained thermodynamic results are compared with existing experimental data and models which can be interpreted thermodynamically. It is concluded that critical phenomena in cerium correspond to critical behavior of the first type.Dnepropetrovsk State University Dedicated to the 300th Anniversary of the Unification of the Ukraine with Russia.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 66–70, May, 1991.     

Positron annihilation in ionic media and an optical model of the positron

It is proposed that positron motion in quasiatomic positron + anion systems formed in anionic media can be described by a potential of the form V_eff(r) = Z_eff/r²-/r, where Z_eff is the effective charge of the nucleus, and n is the effective charge of the anion. It is shown that the positron wave function of the ground state of the quasiatomic positron + anion system in the field of such a potential is _X(r) = l/4·A_nx·r^X·e^–ar. Thus the validity of selecting a test variation positron wave function (r) = l/4·A·r·e^–ar is demonstrated for the potential V_eff = at r = 0 and V_eff = –/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela,8, 515 (1966)), belonging to the class of functions _X(r). Having the wave function _X(r) and Slater wave functions _ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes _ns,p.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–56, May, 1990.     

On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

Differential equations in the spectral parameter

We determine all the potentialsV(x) for the Schrödinger equation (– _x ² +V(x))=k² such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formB(k, _k )ø=(x)ø. For each suchV(x) we determine the algebra of all possible operatorsB and the corresponding functions (x)This research was partially supported by NSF grant DMS 84-03232 and ONR contract NOOO14-84-C-0159     

On the dependence of the coercive field of BaTiO3 single crystals on their thickness

The paper gives the results of measuring the coercive field of single-domain single crystals of BaTiO₃, the thickness of which was lowered by successive etching. The initial decrease in the thicknessd is accompanied by a sudden increase in the coercive fieldE _c (E _c /d –1·5 × × 10⁵ V/cm²); after etching off layers larger than 10^–3 ÷ 2×10^–3cm the coercive field grows much more slowly (E _c /d –7×10³ V/cm²). The high initial growth ofE _c is interpreted by means of Schottky exhaustion layers with non-zero gradient of the electric potential.In conclusion, the authors would like to thank H. Arend, P. Coufová and J. Jarý for providing high-quality single crystals and for much valuable advice during the work and V. Dvoák and K. Pátek for remarks on this paper.     

Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution

In the study of the formulation of Maxwellian tails the nonlinear partial differential equation ² u/x +u/x+u ²=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.     

Energy Spectra of the Local States in the Forbidden Gap of Monoclinic TlInS2xSe2(1?x) Crystals

Near IR properties of the mixed TlInS_2xSe_2(1–x) have been studied previously by the present authors. In this work the temperature and frequency dependence's of the conductivity and the current-voltage characteristics (in relatively weak electric field), have been investigated for monoclinic TlInS_2xSe_2(1–x) crystals, which are perspective materials for IR applications. From the temperature dependence's of conductivity in the direction perpendicular to c- axis the band gap E^g = 2.22 eV was determined for --TlInS₂ crystals. The impurity centres were determined located at 0.43, 0.73 eV and 0.35, 0.48, 1.12 eV for the direction of current i//c and i c, respectively. The concentration of the centres located at 0.48 and 1.12 eV were calculated to be N_A – N_D = 4.8 · 10⁹ cm^–3 and 1.9 · 10¹¹ cm^–3, respectively. It was found that in the solid solutions TlInS_2xSe_2(1–x) for 0.3 x 1, the conductivity follows the dependence (v) = ₀·^s in the temperature range between 100 to 600 K. In the temperature range of 80-400 K charge bounce plays an important role in the conductivity mechanism. Occurrence of the deep and low-levels impurity centres and a tail of the density of energy states in TlInS_2xSe_2(1–x) crystals make them perspective for practical applications: switching and memory effects, N-type current-voltage characteristics, induced conductivity etc.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Effective Stimulated Emission Cross-Sections of Poly(Phenylene Vinylene) Copolymers in Toluene Solution

We report optical gain measurements in four different copolymers polyp-phenylene-co-[2,5-dioctyloxy-p-phenylene-bis-2(4-nonyl phenyl) vinylene]nonyl-PpPV, polym-phenylene-co-[2,5-dioctyloxy-p-phenylene-bis-2(4-methyl phenyl) vinylene]methyl-PmPV, polyp-phenylene-co-[2,5-dioctyloxy-p-phenylene-bis-2(4-methyl-phenyl) vinylene]methyl-PpPV, polyp-phenylene-co-[2,6-naphthylene-bis-2(4-nonyl phenyl) vinylene]nonyl-PpPV-NV in toluene. The copolymers are related to poly(phenylene vinylene) and have been synthesized via Horner–Emmons polycondensation reaction. The optical gain determined from the amplified spontaneous emission (ASE) intensity is dependent on the excited stripe length. The net optical gain coefficients are found to vary between 0.1 cm^–1 in nonyl-PpPV to 2.5 cm^–1 in methyl-PmPV under nanosecond pulse excitation. The gain for Rodamine 6G was also measured under the same experimental condition and was used to determine the stimulated emission cross-sections for the four polymers and found to be _SE(peak)= 6.7 × 10^–20 cm² for nonyl-PpPV, _SE(peak)= 1.7 × 10¹⁸ cm² for methyl-PmPV, _SE(peak)= 1.4 × 10^–18 cm² for methyl-PpPV, and _SE(peak)= 1.5 × 10^–18 cm² for nonyl-PpPV-NV.     

Properties of MOS-structures based on anode-oxidized CdSnAs2

The properties of metal (Al, Au)-anodic oxide-CdSnAs₂ monocrystal structures are studied. It is established that MOS-structures using undoped CdSnAs₂ crystals show a high positive fixed charge in the anodic oxide (N_S 5·10¹² cm^–2) and high surface state density on the oxide-CdSnAs₂ boundary surface (N_SS 2·10¹³ cm^–2·eV^–1). In MOS-structures using diffusion-doped (copper) crystals the sign of the fixed charge is negative (N_S 10¹¹ cm^–2, N_SS 2·10¹² cm^–2·eV^–1). The latter structures show a definite photosensitivity and photomemory. The possibility of effective control of the fixed charge value within the oxide by illumination is shown. The surface state distribution over energy, time constant, and capture section is determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 90–93, September, 1982.     

On the Lax representation for the nonlinear evolution equations

By the classical differential geometry techniques it is shown that a general partial differential equation of the second order with two independent variables can be represented in the Lax operator form [X ₁ X ₂]=0, whereX _i =/x _i – ⁱ ,i=1,2 and ⁱ are the 3×3 matrices. The problem of the introduction of the spectral parameter in this representation is shortly discussed.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.The author is pleased to thank V. K. Mel'nikov for the discussion of this work.     

Die Magnetische SuszeptibilitÄt von Kristallinem n-CdGeAs2

The specific magnetic susceptibility of polycrystalline and powdered samples was measured between 77 °K and 570 °K. This dependence was interpreted in intrinsic range suggesting the susceptibility is given as a sum of contributions of the lattice ^G and of free carriers _L. The temperature dependence of the lattice susceptibility _G= _G ⁰ +T was checked: _G ⁰ =–2·35× ×10^–7, =4·5×10^–11. The contribution _L enabled to check the effective mass of holes m_h=0·25m₀ suggesting m_em_h.

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Herrn A. Hrubý gilt mein Dank für die Vorbereitung des polykristallinen Ingots von CdGeAs₂.     

Cross-section asymmetry for the reactions γd →pn, γd → π0 d by linearly polarized photons in the energy rangeE γ = 0·4 – 0·8 GeV

The beam asymmetryB has been measured for the reactiond pn in the energy rangeE = 0·4 ÷ 0·8 GeV and angles _p ^cm = 45 ÷ 95° and ford ⁰d at energiesE =0·5, 0·6, 0·7 GeV and angle ^cm = 130°. The results obtained are compared to existing theoretical predictions which take into account the possible contribution of dibaryon resonances.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Influence of the overall pressure on electrical conductivity of the amorphous semiconductor Ge15Te81S2As2

The experimental results obtained with the chalcogenide glass Ge₁₅Te₈₁S₂As₂ with imposed overall pressure up to 700 MPa are presented. The material exhibits the switching effect and the memory effect. It is shown that the overall pressure changes remarkably d.c. electrical conductivity of the amorphous semiconductor. It is assumed that the changes in conductivity are caused by changes in activation energy. The changes in activation energy within the range of considered pressures are, as follows from our measurements, E/p–10·95×10^–5 eV/MPa +p × 10·41 W 10^–7 eV/MPa². The assumption of the activation energy dependence on pressurep are confirmed also by measurements of dependence In vs. 1/T at various pressures.     

Determination of internal scale of artificial ionospheric turbulence in direction of geomagnetic field

A 150-MHz satellite beacon is used to determine the internal scale in the direction of the geomagnetic field I₀ for the spectrum of artificial ionospheric turbulence created by the Yastreb heating facility located near Nizhny Novgorod in continuous operation at a frequency of 5.75 MHz (ordinary polarization) with effective power P·G100·150 kW. It is found that I₀ 3–4 km for transverse inhomogeneity scales I 1–2 km and I 0.7–0.9 km for I 0.5 km.Nizhny Novgorod Scientific-Research Radio-Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 4, pp. 521–525, April, 1994.