Correlation tensors of the blackbody radiation in rectangular cavities

Electromagnetic equilibrium fluctuations in finite cavities filled with a dissipative medium (dielectric function ()=+i) and bounded by walls of infinite conductivity are considered. Expanding the fields in terms of a complete and orthonormal set of functions and solving the Maxwell equations the response of the EM field to external forces (polarization and magnetization) is obtained. With the aid of the fluctuation dissipation theorem and the linear response functions the 2nd order correlation tensors of the EM field are derived.For rectangular cavities explicit considerations are made. In the case of transparent media (=0) the spectral energy density of the EM radiation is calculated.     

Fine Structures of the Permittivity and Characteristic Losses of Electrons in Fluorite

Experimental-computational spectra of the permittivity and characteristic losses –Im^–1 for energies in the range 5–21 eV at a temperature of 4.2 K and theoretical spectra of and –Im^–1 of a fluorite crystal are resolved into elementary transition bands. The parameters of transition bands (energies of their maxima E _i, band halfwidths H _i and areas S _i, and oscillator forces f _i) are determined. A correlation of the spectral bands of and –Im^–1is established, and their specific features are elucidated.     

s-Polarized nonlinear surface polaritons

An exact solution of Maxwell's equations is found, corresponding to ans-polarized nonlinear surface polarition, at the planar interface between two dielectric media, one of which is optically unaxial and is characterized by a diagonal dielectric tensor whose elements depend on the amplitude of the electric field according to ₁₁=₂₂=₀()+a() (|E ₁|²+|E ₂|²), ₃₃=(). Such modes have no counterpart in the corresponding linear system.     

Colored noise in activated rate processes

We consider bistable systems driven by stationary wideband Gaussian colored noise. We construct uniform asymptotic expansions of the stationary probability density function and of the activation rate, for small intensity and short correlation time of the noise. We find that for different values of the total power output / of the noise, different terms in the asymptotic expansions become dominant. For we recover previously derived results, while for =O() and new results are obtained.     

Automatic measurement of the complex permittivity at millimeter wavelengths

A measuring system including an oversized cavity resonator operating in the TE₀₁ mode for the determination of the complex permittivity - j of low-loss liquids at frequencies of about 36 GHz is described. While is obtained by wavelength measurements in the filled and the empty resonator, is determined from the variation of the Q factor of the filled resonator with the length of the dielectric sample. The Q factors of values of about 2·10⁴ to 10⁵ can be measured automatically by means of a desk calculator which controls the frequency and collects the digitized values of the detector output voltage. By means of the calculator, the Q factors of the resonator are determined by fitting analytical (Lorentzian) resonance curves to the measurement data. and the Q factor for zero sample length are calculated according to Göttmann's methods.     

A stochastic theory of adiabatic invariance

LetI be a set of invariants for a system of differential equations with an ordero() vector field. When order perturbations of zero mean are added to the system we show that, under suitable regularity and ergodicity conditions,I becomes an adiabatic invariant with maximal variations of order one on time scales of order 1/². In the stochastically perturbed case,I behaves asymptotically (for small ) like a diffusion process on 1/² time scales. The results also apply to an interesting class of deterministic perturbations. This study extends the results of Khas'minskii on stochastically averaged systems, as well as some of the deterministic methods of averaging, to such invariants.Supported by NSF grant DMR-8704348     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.     

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co⁵⁹(p,n) reaction forE _p 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni⁵⁹ nucleus were also determined.

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Co⁵⁹(p,n) E _p 6,5 MeV

- Co⁵⁹(p,n) E _p 6,5 MeV. , 50%. , Ni⁵⁹.

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The authors would like to thank all those who helped in this work, particularly all members of the cyclotron group of the Nuclear Research Institute of the Czechoslovak Academy of Sciences, who so willingly helped with the irradiation, and H. Koutová from the Faculty of Technical and Nuclear Physics, who carefully measured the emulsions. Our thanks are also due to R. Krejová from the Faculty of Technical and Nuclear Physics for developing the emulsions and J. Kopecký from the Nuclear Research Institute for providing the cobalt target.     

Dielectric constant characterization of large-area substrates in millimeter wave band

A possibility of the dielectric constant measurement for substrates with permittivity=+i without an essential restriction on their area has been shown experimentally. The method uses frequency measurement of quasioptical dielectric resonator (QDR) with two slots oriented along the QDR radius with a dielectric substrate in one of them. Taking QDR of teflon in 8mm waveband as an example it is found that measurable values of can ran up 15 _q , where _q is the QDR material permittivity. Absolute error of the measurements is determined by an accuracy with which the permittivity of calibrated (standard) samples is known. The relative measuring error is determined by the accuracy of the QDR frequency measurement and can be quite a small. As an example the method is demonstrated forLaAlO ₃ single crystals.     

A stochastic particle system modeling the Carleman equation

Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient >0 but different velocities (drift), 1 for one species and –1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance ( being a positive parameter), they both may simultaneously flip their velocity according to a Poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when goes to zero and the total number of particles increases like ^–1. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, depends on and suitably vanishes when goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.Dedicated to the memory of Paola Calderoni.     

Photonic pseudogaps for periodic dielectric structures

We consider the problems of existence and structure of gaps (pseudogaps) in the spectra associated with Maxwell equations and equations that govern the propagation of acoustic waves in periodic two-component media. The dielectric constant is assumed to be real and positive, and the value of = _b on the background is supposed to be essentially larger than the value of = _a on the embedded component. We prove the existence of pseudogaps in the spectra of the relevant operators. In particular, we give an accurate treatment of the term pseudogap. We also show that if the contrast _b / _a approaches infinity, then the bands of the spectrum shrink to a discrete set which can be identified with the set of eigenvalues of a Neumann-type boundary value problem and thus can be effectively calculated.     

Electron velocity and momentum density

A null 4-vector ^°, based on Dirac's relativistic electron equation, is shown explicitly for a plane wave and various Coulomb states. This 4-vector constitutes a mechanical model for the electron in those states, and expresses the important spinor quantities represented conventionally byn, f, g, m, j, ,1, ands. The model for a plane wave agrees precisely with the relation between velocity and phase gradient customarily used in quantum theory, but the models for Coulomb states contradict that relation.     

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping _H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=^-1H, which differs fromK, but turns out to be ⁵ close to it. Special attention is devoted to numerical integration for scattering problems.     

Periodic Thermodynamics

This paper develops the thermodynamics of quantum Floquet systems, i.e., quantum systems driven by an arbitrarily strong periodic perturbation, which are in weak interaction with a heat bath. The physics differs in an essential way from that of undriven systems, because the usual energy conservation law, for interactions between the system and heat bath, is changed to +E=0, ±, ±2,... where is the driving frequency, is the difference of the so-called quasi-energies of the Floquet states and E the excitation energy of the bath. That is, a transition between two given physical Floquet states will be accompanied by bath transitions with many different energy changes, E=–+m, where m is an arbitrary integer. This results in a breakdown of detailed balance. There is a steady state in which the system has periodic fluctuations of period T=2/. The steady state density matrix is diagonal in the Floquet states, with all Floquet states having finite weights, even at zero temperature. Experimentally favorable conditions for studying periodic thermodynamics are briefly discussed.     

Electronic structure and optical spectra of YBa2Cu3O7−δ thin films in the infrared and UV region

Optical reflectance of YBa₂Cu₃O_7- thin films grown by laser ablation is measured within photon energies of 0.1 eV to 3.5 eV at room temperature. The spectra can be fit congruently with the anisotropic dielectric constants which take account of the intraband free carrier transition and interband transition. The anisotropic plasma frequencies are simulated to be _pl=2.18 eV and _ch=2.80 eV contributed from free carriers on the plane and in the chain, respectively. The interband transition occurs near 2.5 eV and is pertinent to a rather broad line width.     

The slow passage through a steady bifurcation: Delay and memory effects

We consider the following problem as a model for the slow passage through a steady bifurcation: dy/dt = (t) y – y³ +, where is a slowly increasing function oft given by= _i + t ( ⁱ,<0). Both and are small parameters. This problem is motivated by laser experiments as well as theoretical studies of laser problems. In addition, this equation is a typical amplitude equation for imperfect steady bifurcations with cubic nonlinearities. When=0, we have found that=0 is not the point where the bifurcation transition is observed. This transition appears at a value = ^j > 0. We call ^j the delay of the bifurcation transition. We study this delay as a function of ⁱ, the initial position of, and, the imperfection parameter. To this end, we propose an asymptotic study of this equation as 0, small but fixed. Our main objective is to describe this delay in terms of the relative magnitude of and. Since time-dependent imperfections are always present in experiments, we analyze in the second part of the paper the effect of a small-amplitude but time-periodic imperfection given by (t) = cos(t).     

First order phase transitions studied in the dynamical ensemble

A knowledge of the density of states () of a many particle system ( is the energy per particle) contains the complete information about its thermal behaviour. In this paper it will be demonstrated that () can very efficiently and precisely be determined by a Monte Carlo calculation in an ensemble where the system of interest is coupled to another system of comparable size. This is in contrast to the canonical approach where the system of interest is coupled to an infinite bath at a temperatureT. The usefulness of the approach will be demonstrated for theq-states Potts model withq=4, 5, and 8 where the numerical data can be compared with exact results. In our numerical data we can clearly identify a first order phase transition forq5 and a second order transition forq=4.     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

Study of the influence of iron and lanthanum oxides on the band structure of Pb(Zr,Ti) O3

The measurements of diffuse reflectance spectra in the range of 400; 2500 nm and of photoacoustic spectra in the range of 350; 800 nm were used for the study of the influence of iron (III) oxide and lathanum oxide additions on the band structure of polycrystalline lead zirconate — lead titanate solid solutions. The molar ratio of zirconium and titanium in the studied solid solutions was 60 40, and the concentrations of the dopants werex FeO_1.5, andy LaO_1.5, werex 0; 0·05 mol, andy 0; 0·10 mol, respectively. The diffuse reflectance spectra were expressed in terms of the Kubelka-Munk function values versus incident electromagnetic radiation energy. These dependences were decomposed into partial absorption bands using a computer. Transitions of charged carriers between energy levels or bands which differ mutually by the energy of 0·9, 1·2–1·3, 1·6, 1·65–1·7, 2·4–2·5, 2·75–2·8, 2·9–3·2, 3·4–3·8 eV, were identified. Their intensities depend on the concentration of Fe and/or on La in the Pb(Zr_0.60 Ti_0.40) solid solutions.The authors are very grateful to Mrs. Iva Havlasová, Vra Andrsová, Ing. Jan Netuka, and Mrs. Liana Karlíková from the first authors' institute, for their technical assistance.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.