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.     

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.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

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.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.     

Fluctuations of intensity and arrival angles for light waves in spatially-limited collimated beams in a turbulent atmosphere

This paper presents results of an experimental investigation of fluctuations of intensity and arrival angle as a function of the parameter = ka²/L (where k = 2 /,a is the beam radius, and L is the length of the track) for tracks of different lengths. It is shown that, depending on the value of ₀ ² = 1.23 C _n ² k^7/6 L^11/6, the intensity fluctuations can both increase, and also decrease with increase of . The fluctuations of arrival angle have a maximum for beams for which the parameter 5.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 108–112, September, 1973.     

Overview of partial orientational and positional ordering in concentrated systems

We present experimental results for Taylor-Couette flow subjected to a Coriolis force. We used an apparatus consisting of two concentric cylinders with the inner one rotating, and with a radius ratio near 0.75. It was mounted with its axis horizontal on a table which rotated with angular velocity about a vertical axis. For sufficiently low, the first bifurcation upon increasing the inner-cylinder rotation rate was to tilted vortices. With further increase in this bifurcation was followed by a secondary one to time-periodic tilted vortices. The two bifurcation lines met at higher. The initial bifurcation then became one to tilted traveling vortices. For even larger values of, the flow immediately above the initial transition was disordered, and for sufficiently large the initial bifurcation was to a featureless turbulent state. We studied these transitions with three different outer cylinders. Two had symmetric spatial ramps terminating both ends of a straight section to reduce the effect of the rigid, nonrotating ends, and one had no ramps. The transition to featureless turbulence in the apparatus with ramps became hysteretic over a range of.     

Iterated networks and the spectra of renormalizable electromechanical systems

Beginning with anLRC network with impedance functionZ(), a sequence of iterated networksN _k with impedance functionsZ ^k(), k= 1, 2, 3,..., is introduced. The asymptotic comportment ofZ ^k() and the spectra ofN _k are analyzed in terms of the Julia set ofZ. An example is given of an iterated network associated with a cascade of period-doubling bifurcations.     

Poisson–Lie Diffeomorphism Groups

We explicitly construct a class of coboundary Poisson–Lie structures on the group of formal diffeomorphisms of ⁿ . Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra W _n of formal vector fields on ⁿ . We conjecture that this class accounts for all such coboundary structures. The natural action of the constructed Poisson–Lie diffeomorphism groups gives rise to large classes of compatible Poisson structures on ⁿ , thus making it a Poisson space. Moreover, the canonical action of the Poisson–Lie groups FDiff( ^m ) × FDiff ⁿ ) gives rise to classes of compatible Poisson structures on the space J ( ^m , ⁿ ) of infinite jets of smooth maps ^{m n} , which makes it also a Poisson space for this action. Poisson modules of generalized densities are also constructed. Initial steps towards a classification of these structures are taken.     

Multicomponent composites,electrical networks and new types of continued fraction I

The development of bounds on the complex effective conductivity tensor * (that relates the average current to the average electric field in a multicomponent composite) has been hindered by lack of a suitable continued-fraction representation for *. Here a new field equation recursion method is developed which gives an expression for * as a continued fraction of a novel form incorporating as coefficients the component conductivities and a set of fundamental geometric parameters reflecting the composite geometry. A hierarchy of field equations is set up such that the solutions of the (j+1)th-order equation generate the solutions of thejth-order equation. Consequently the effective tensor ^(j) associated with thejth-order field equation is expressible as a fractional linear matrix transformation of ^(j+1). These transformations combine to form the continued fraction expansion for *=⁽⁰⁾ which is exploited in the following paper, Part II, to obtain bounds: crude bounds on ^(j), forj1, give narrow bounds on *. The continued fraction is a generalization to multivariate functions of the continued fraction expansion of single variable Stieltjes functions that proved important in the development of the theory of Páde approximants, asymptotic analysis, and the theory of orthogonal polynomials in the last century. The results extend to other transport problems, including conduction in polycrystalline media, the viscoelasticity of composites, and the response of multicomponent, multiterminal linear electrical networks.     

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.     

A generalization of Dyson's formula

We give an integral representation for tempered distributions which have more general support properties inx space, than those usually assumed in the derivation of the Dyson formula.The existence of such an integral representation is shown to be equivalent to that of a suitable extension of an analytic function: namely, given an analytic function on a section of a domain of holomorphy extend it to imposing on it some growth conditions. L ² space methods ofL. Hörmander are used to solve this problem of extension. In order to apply these Hilbert space techniques, it was necessary to prove two important theorems on the growth of analytic function.From the physical point of view the formula we obtained is an integral representation for the commutator of two quasi local fields.     

Harmonic maps with defects

Two problems concerning maps with point singularities from a domain C ³ toS ² are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by holes, ³,S ² is replaced by ^N ,S ^N–1 or by ^N , P ^N–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02     

The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.     

Deformation Quantization with Traces

In this Letter we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a constant volume form and a Poisson bivector field on ^d such that div=0, the Kontsevich star product with the harmonic angle function is cyclic, i.e. (f*g)·h·= (g*h)·f· for any three functions f,g,h on (for which the integrals make sense). We also prove a globalization of this theorem in the case of arbitrary Poisson manifolds and an arbitrary volume form, and prove a generalization of the Connes–Flato–Sternheimer conjecture on closed star products in the Poisson case.     

Dark Energy and Global Rotation of the Universe

We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory _r,0 can be identified with ^,0 (only dust fluid is admissible) and rotation can exist with _r,0 =^,0 0. However, the best-fit flat model is the model without rotation, i.e., ^,0 =0. In the considered case we obtain the limit for ^,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are _m,0 ~ 0.3, _r,0 ~ 10^-4, then the SN Ia data show that ^,0 -0.01 (or ₀ > 2.6 · 10^-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is _r,0 ( - 0.01, 0.04).     

Renormalization group study of anomalous acoustic behavior in critical percolation network

We study the acoustic behavior of critical percolation network within a real-space renormalization group framework recently proposed by Ohtsuki and Keyes. Using large cell Monte Carlo renormalization group calculations, we obtain the exponent for anomalous sound dispersion K ^1+x/v . Our estimate 2x/v0.80 is in agreement with the exponent for anomalous diffusion in percolation clusters =(–)/v.     

On the second eigenfunctions of the Laplacian in R2

A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain by intersecting with the boundary of transversely, where is a bounded convex domain ofR ². We prove this conjecture provided has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided is a bounded convex domain ofR ².Supported in part by NSF DMS 84-09447Home Institution: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA     

Some properties of a collision term of a kinetic equation in a magnetic field

The collision term of a Fokker-Planck type kinetic equation is derived for the case of a two component magnetized plasma. It is shown that the collision processes are fully described by one symmetric two-dimensional dyadicQ. The collision term is modified for the case in which the distribution function of the field particles is Maxwellian.Conditions under which the magnetic Rosenbluth potentials can be introduced are studied. It is shown, in case that the distribution function of the field particles is Maxwellian, that the coefficients of friction and diffusion are expressible in terms of two scalar potentials only if _a = 0 or if the components D and D of the difusion coefficient are constant with respect to _a , for arbitrary _b of the field particles.