Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

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.     

2- And 3-cochains in 4-dimensional SU(2) gauge theory

Explicit formulae are derived for the 2- and 3-cochains _uvq ⁽²⁾ (i, j, k) and _uvq ⁽²⁾ (i, j, k, ) in SU(2) gauge theory in 4 dimensions. It turns out that _uvq ⁽²⁾ (i, j, k, ) is given by the volume of a spherical tetrahedron spanned by the gauge transformations relating the gaugesi, j, k, l.     

The quasilinear theory of two-stream cyclotron instability of electron beams

The paper is devoted to a study of cyclotron instability ( _e) of two opposite beams of electrons from the aspect of the quasilinear effects. For this case of instability the authors evolve the diffusion equation in the velocity space for an averaged distribution function. They estimate the relaxation times , _z of the spreading of the distribution function in the velocity space. At the end of the paper, they compare their results with an experiment described by M. Seidl and P. unka [Phys. Letters11 (1964), 31].     

Self-precession and frequency shifts for three interacting waves for a nonlinear model equation in a dispersive medium

The wave-wave interaction of three interacting waves for a nonlinear model equation in a dispersive medium is studied. It is found that the nonlinear effect causes precession of the polarization ellipse as the wave propagates under the resonance condition ₁ = ₂ + ₃ and k₁ k₂ + k₃. The frequency shifts and the precessional frequencies are obtained under the above resonance conditions. A technique has been developed for the evaluation of self-precession and frequency shifts for circularly polarized waves.The author expresses his gratitude to Dr. B. Chakraborty, Department of Mathematics, Jadavpur University, Calcultta for his guidance in the preparation of this paper and also to the referee for his suggestion in the improvement of this paper.     

Relations between Black Hole Spin and Angular Velocity of Accreting Particles near the Horizon

Evolution characters of angular velocity _H of a Kerr black hole (BH) and distribution characters of angular velocity _p of accreting particles near the BH horizon are investigated in the case of thin and thick disks, respectively. It is shown that _H evolves in a non-monotonous way in the case of thin-disk-pure-accretion, attaining a maximum at a _* 0.994. This evolution character turns out to depend on the radial gradient of _p near the BH horizon. It is proved that both quantities, ( d_H /dt) _ms and ( _p /r)_{r=r H}, vanish at the same value of a _*: a _*0.994, and an explanation for the non-monotonousness of _H is provided.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

The thermodynamic limit for a crystal

Consider a crystal with nucleii fixed at the lattice points in ³, interacting by Coulomb forces with quantized electrons in . We prove that the pressure tends to a limit as grows infinitely large.Supported by NSF Grant No. MCS80-03072     

Reactive pulsed laser deposition and laser induced crystallization of SnO2 transparent conducting thin films

Transparent conducting SnO₂ thin films with a thickness between 1000–2000 Å were deposited on glass, quartz and silicon substrates using standard pulsed laser deposition techniques with two different targets (Sri and SnO₂) and with three different laser wavelengths (1.06, 0.532 and 0.266 ) from a Q-switched Nd: YAG laser. Tin dioxide films with optical transmission over most of the visible spectrum exceeding 80% were obtained using a Sn target and a background oxygen pressure of 20 Pa. The electrical resistivity () depended strongly on the substrate temperature during deposition, with the lowest values of of about 10^–2 -cm obtained when the substrate was maintained at 400°C during deposition. Using SnO₂ targets, predominantly amorphous phase SnO₂ films were deposited on Si substrates and then transformed into polycrystalline Sn₃O₄ by laser induced crystallization ( = 1.06 m). Whereas these later films were essentially non-conducting as deposited ( > 400 -cm), the electrical resistivity was permanently reduced after laser induced crystallization by a factor greater than 1000 to a value of approximately 4 × 10^–1 -cm.     

Inverse Problem for a General Bounded Domain inR3 with Piecewise Smooth Mixed BoundaryConditions

We study the influence of a finite container on an ideal gas. The trace of theheat kernel (t) = _{= 1}exp(–t), where {} _{= 1}are the eigenvalues of the negative Laplacian – ² = – ³ _{= 1}(/x )² in the (x ¹, x ², x ³)-space,is studied for a general bounded domain with a smooth bounding surface S, where afinite number of Dirichlet, Neumann, and Robin boundary conditions on thepiecewise smooth parts S _i (i = 1, ..., n) of S are considered such that S =U _{i = 1} S _i . Some geometrical properties of (the volume, the surface area, the meancurvature, and the Gaussian curvature) are determined. Furthermore,thermodynamic quantities, particularly the energy, for an ideal gas enclosed inthe general bounded domain with Dirichlet, Neumann, and Robin conditionsare examined with the help of the asymptotic expansions of (t) for short timet. We show that these thermodynamic quantities depend on some geometricproperties of .     

Probabilistic formulation of classical mechanics

Starting axiomatically with a system of finite degrees of freedom whose logic _c is an atomic Boolean -algebra, we prove the existence of phase space _c, as a separable metric space, and a natural (weak) topology on the set of statesI (all the probability measures on _c) such that _c, the subspace of pure statesP, the set of atoms of _c and the spaceP( _c) of all the atomic measures on _c, are all homeomorphic. The only physically accessible states are the points of _c. This probabilistic formulation is shown to be reducible to a purely deterministic theory.     

Conditional stability of multiple-charged solitons

The stability of the three-dimensional multiple-charged soliton solutions to the nonlinear field equations is studied by Lyapunov's method. It is proved that an absolutely stable soliton solution can not exist in any field model. By imposing the subsidiary condition ^pQ_i=0 (fixation of charges) we find a sufficient condition for stability of the stationary soliton which includes the inequality ^{k i} (Q ⁱ / ^k <0. An illustrative example is considered.     

An accelerated closed universe

We study a model in which a closed universe with dust and quintessence matter components may look like an accelerated flat Friedmann–Robertson–Walker (FRW) universe at low redshifts. Several quantities relevant to the model are expressed in terms of observed density parameters, _M and , and of the associated density parameter _Q related to the quintessence scalar field Q.     

Conformal quantum field theory and half-sided modular inclusions of von-Neumann-Algebras

LetN, be von-Neumann-Algebras on a Hilbert space , a comon cyclic and separarting vector. Assume to be cyclic and separating also forN . Denote byJ , J _N the modular conjugations to (, ), and _N the associated modular operators. If and these data define in a canonical way a conformal quantum field theory in a cricle. Conversely, the chiral part of a conformal quantum field theory in two dimensions always yields such data in a natural way.Partly supported by the DFG, SFB 288 Differentiageometrie und Quantenphysik     

Convective excitation of quasistatic waves in an inhomogeneous anisothermic plasma II. Nonlinear estimates

Nonlinear effects stabilizing the convective instabilities excited in an anisothermic plasma (T _etT _i) at the plasma boundaryaV_s/ _Bi) are discussed. Waves having in the linear theory (Part I) the highest growth rates ( _Bi) saturate at first. Being excited by a small part of slow plasma electrons ( _zTe) only, they saturate at a relatively low level. Further, surface waves with lower frequencies and higher phase velocities ( _ph/k_z) become dominant and a broadening of the plasma boundary occurs. For their saturation nonlinear interaction is more important than the quasilinear effects. During the time interval of several _Bi ^–1 the longest surface waves withk _yBi/V_s, _Bik_yV_s and _{ph Te} saturate at the absolutely highest level. The plasma boundary broadens in the meanwhile up toaV _s/_Bi. The wave energy is comparable to the whole energy connected with the longitudinal motion of the initially thermal electrons inside this boundary layer. The wave amplitude is large enough to trap the initially cold ions belonging to this layer and heat them up to energies comparable to those of the electron component. The heating process occurs again within several _Bi ^–1 and the Larmor radius of the ions is then comparable toV _s/_Bi. Further evolution of the system is governed by the unstable local perturbations.He leaves of absence from thePhysical and Technical Institute, Kharkov, USSR.     

Inflation, Extra Dimensions, and ΩΛ ≈ 1

An (N + 1)-dimensional quantum mechanical model for the origin of the universeresults in a 58e-fold inflation and a cosmological constant/vacuum energy densitywith 1.     

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.     

Spectral properties of certain composition operators arising in statistical mechanics

By applying the theory of linear positive operators in a Banach space we derive spectral properties of certain composition operators in the Banach spaceA () of holomorphic functions over some domain . Examples of such operators are provided by the so called generalized transfer matrices of classical one-dimensional lattice systems.     

Field of View Increase for Optical Heterodyne Receivers

The field of view of optical heterodyne systems are usually limited by a simple criterion- namely, that A_RR ², where A_R is an effective aperture, _R the corresponding field of view and the optical wavelength. This paper will demonstrate that with a simple change of systems geometry and the possible use of array detectors, this severe restriction can be alleviated considerably and, in some cases, eliminated. Both coherent sources and thermal radiation sources are considered. This might suggest that heterodyne systems that were eliminated in the past because of that criterion alone, could turn out to be, not only possible, but even advantageous compared to other techniques.