Normal mode configuration in an inorganic medium containing defects

The vibrational structure in an inorganic medium containing defects is analyzed as a function of the frequency of the applied field. Since the dispersion relations for the medium are nonlinear, the configuration of the normal modes depends differently upon and . It is shown that exponential damping of the optic branches is observed for <₀, and that the structure of these modes changes significantly over the range 0<<₀, so that only in the neighborhood of ₀ does it correspond to long wavelength vibrations with configurations of stress deviator waves.Institute for the Physics of Strength and Materials Science, Russian Academy of Sciences, Siberian Division. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–90, October, 1994.     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Effective method of phase conjugation of multifrequency radiation in “pseudo”-four-wave interaction

The possibility is considered of formation of a multifrequency-radiation wave front (with a wide line spectrum in the interval , +), reversed with respect to the wave front of a signal wave of frequency ₀ unequal to the frequencies in the indicated spectrum. The wave front reversal (phase conjugation) is achieved by diffraction of a multifrequency light wave in a direction counter to that of the signal, on a three-dimensional dynamic hologram produced by electromagnetic fields of frequency ₀ in a resonant medium (with thermal nonlinearity) that is fully transparent to the multifrequency radiation. A single direction of the radiation diffraction at all frequencies of the spectrum is ensured by preliminary passage of the initial multifrequency wave through a simple dispersive prism that deflects the direction in each spectral line in proportion to the frequency change. The basic equations describing a similar phase conjugation method are derived, and the efficiency of the conjugation are estimated using as an example multifrequency emission of a chemical cw HF laser.P. N. Lebedev Instiute of Physics. Translated from Preprint No. 205 of the lebedev Institute of Physics of the Academy of Sciences of the USSR, Moscow, 1989.     

Flow of an elastico-viscous fluid past an oscillating plate

An exact solution for the flow of an elastico-viscous fluid (Walters' liquid B') due to an oscillating infinite plate has been derived. It has been observed that forgwt=0, ( — frequency,t — time) the flow near the plate may become unstable with increasing whereas fort>0, the velocity increases with increasing. The shearing stress decreases with increasing.I wish to thank the referee for his useful comments which led to the improvement of this paper.     

The incoherent scattering function and related correlation functions in hard sphere fluids at short times

For a classical fluid of hard spheres and hard disks exact expressions for all densities and wave vectors are derived for the coefficients oft ⁿ in the short-time expansion of the incoherent intermediate scattering function (n = 0, 1,..., 4) and the velocity correlation function (n=0,1,2). Similarly, we obtain the coefficient of the leading term in the short-time behavior of the cumulants of the displacements. Furthermore,S(k, ) has a high-frequency tail ^–4, characteristic for the hard-sphere fluid, which leads to a modification of the standard sum rules. We present estimates for the frequency range, in which this tail may be observed in neutron scattering off noble gases. The results are also compared with Enskog's theory and molecular dynamics calculations.     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Classical “freezing” of plane rotations: A proof of the Boltzmann-Jeans conjecture

Using simple known methods and results of classical perturbation theory, especially those due to Nekhoroshev and Neishtadt, we study the energy exchanges between the rotational and the translational degrees of freedom in a particular model representing the planar motion of a rigid body in a bounded analytic potential. We prove that, if the angular velocity is initially large, then the energy exchanges are small,O( ^–1), for times growing exponentially with, |t|exp. We also deduce that in a scattering process from a (smooth) potential barrier, the overall change in the rotational energy of the incoming body is exponentially small in, exp(–. The results are interpreted in the light of an old conjecture by Boltzmann and Jeans on the existence of very large time scales for equilibrium in statistical systems containing high-frequency degrees of freedom (purely classical freezing of the high-frequency degrees of freedom); the rotating object is, in this interpretation, a (classical) molecule, which moves in an external field, or collides with the wall of a container. Two different limits of large are considered, namely the limit of large rotational energy, and (as is interesting for the molecular interpretation) the limit of point mass, at finite rotational energy.     

Four-wave mixing in alkali halide crystals and aqueous solutions

Noncollinear phase-matched nonresonant four-photon frequency mixing _p+ _p– _{L s} in crystals and aqueous solutions of LiCl, CsCl, KF, and KI is studied. The concentration of the aqueous solutions is varied between 0.5 mol/l and saturation. Picosecond laser pulses of a mode-locked Nd-glass laser are applied as pump pulses. The energy conversion of laser light at frequency _L to frequency _S is measured and the nonlinear susceptibilities ⁽³⁾ are calculated. The dependence of the hyperpolarizabilities on concentration is analysed and gives information on the solute-solvent interaction.     

Collective modes,damping, and the scattering function in classical liquids

An exact representation for the density-density response function is presented. This representation is a generalization of the result obtained in the mean field approximation and amounts to replacing the static, effective potential by one which is both wavenumber- and frequency-dependent. This potential possesses both a real and an imaginary part; the latter describes the collisional damping of collective modes. Analyticity and sum rule arguments are used to describe the basic properties of this complex potential. The formalism allows us to write an exact formula for the scattering functionS(k, ) in which the basic unknown is the collisional damping function. Using a small portion of the recent experimental data on coherent neutron scattering in liquid argon, we are able to calculateS(k, ) and other quantities of interest and to make comparisons with the rest of the data.     

Homogeneous and hypersurface-homogeneous shear-free perfect fluids in general relativity

Shear-free, general-relativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurface-homogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density and the presurep of the fluid are related by a barotropic equation of statep = p(), where +p 0. Under such circumstances, it follows that either the fluid's volume expansion rate or the fluid's vorticity (i.e., rotation) must vanish. In the homogeneous case, this leads to only two possibilities: either = = 0 (the Einstein static solution), or 0, = 0 (the Gödel solution). In the hypersurface-homogeneous case, the situation is more complicated: either = 0, 0 (as exemplified,inter alia, by the Friedmann-Robertson-Walker models), or 0, = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or = = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.     

Two-photon resonance degenerate four-wave mixing in a three-level polar molecule (model calculations)

The third-order non-linear susceptibility, ⁽³⁾(; , , –), describing the phase conjugation by degenerate four-wave mixing (DFWM) is calculated for a three-level polar system under a two-photon resonance (TPR) condition. The part of the susceptibility expressed only by the transitional dipole moments and the part resulting from the permanent dipole moments are distinguished. The spectra of ⁽³⁾(; , , –), as well as the DFWM power-reflection and power-transmission spectra near to the TPR, are modelled for polar molecules. The effect of enhanced reflectivity of TPR-DFWM is obtained numerically.     

The Schrödinger equation and canonical perturbation theory

LetT ₀(, )+V be the Schrödinger operator corresponding to the classical HamiltonianH ₀()+V, whereH ₀() is thed-dimensional harmonic oscillator with non-resonant frequencies =(₁, ... , _d ) and the potentialV(q ₁, ... ,q _d) is an entire function of order (d+1)^–1. We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schrödinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schrödinger series near any eigenvalue ofT ₀(, ) admits a convergent expansion in powers of of initial point the corresponding term of the classical Birkhoff expansion. Moreover ifV is an even polynomial, the above result and the KAM theorem show that all eigenvalues _n (, ) ofT ₀+V such thatn coincides with a KAM torus are given, up to order , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in .     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

Effect of gravitational radiation upon electromagnetic waves in a dispersive medium

We show that linearized gravitational radiation produces fluctuations in intensity and position of a distant source if the ray travels in a dispersive medium. The effect, however, depends upon the nongeodesic character of the ray and does not occur in an electrostatic plasma. When the index of refraction n is greater than unity a Cerenkov type resonance produces scintillation proportional to D _O ^3/2 (D _O being the distance of the source) and a dancing proportional to D _O ^1/2 if, instead, n<1 the scintillation behaves like D _O and the dancing does not diverge as D _O . The calculation is performed in detail for a random and isotropic spectrum of gravitational waves W(). This effect allows one to set an upper limit to W() at the frequency at which the fluctuations are observed, but for the rarified interstellar and intergalactic plasmas these limits are not very interesting.     

Extensible Embeddings of Black-Hole Geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M ₅ × S ₁ (rather than in standard Minkowski M ₆ ) and parametrized by some wave number k, extensibility can be achieved for apparently forbidden frequencies in the range ₁ (k) ₂ (k). As k 0, _{1, 2} (0) _H (e.g., _H = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field.     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.