Linear and non-linear ac response of the stochastic classical model for sliding charge density waves

A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency _OSC inherent in the model. In the present investigation a current noise of strengthT _N proportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: _OSC,T _N ,and a crossover frequency _OSC. Results are evaluated for the ac conductivity (;E ₀,E ) as function of frequency , dc bias electric fieldE ₀ and ac signal field strengthE . ForE 0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =_OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=_OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E ₀,E =0) vs.E ₀, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT _N .The results stress the need for a complete Fokker-Planck treatment sinceT _N is not simply related to the line width.     

Radiation damping of waves in a cold magnetized two-component plasma

It is shown in this paper that the damping decrements of electromagnetic waves with right circular polarization and the decrements of plasma oscillations near the cyclotron and hybrid frequencies in a strong magnetic field _eBpe are proportional to the square of the cyclotron frequencies _eB and _iB. In a weak magnetic field _eBpe the damping decrements of all modes are proportional to the square of the plasma oscillation frequencies _pe, _pi. Taking account of ions results in a nonzero damping decrement for electromagnetic waves with left circular polarization.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 8–11, October, 1982.In conclusion, I am grateful to L. S. Kuz'menkov and P. Polyakov for constant attention to the research and for useful remarks.     

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.     

The Hamiltonian of the guiding centre in the electromagnetic field

The Hamiltonian of the guiding centre in an adiabatically variable electromagnetic field (for the relative variations of the field 1/H. dH/dt _c , 1/E. dE/dt _c ) is derived in the present paper.The solution of the corresponding canonical equations is given for an axially symmetric stationary electromagnetic field.     

Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of electric or magnetic type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an antiparticle. Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (, ₀, ,l, m), where ₀ is the mean of the angular frequencies of the plane waves making up the configuration, is the variance of those frequencies, is a positive constant with dimensions of action, andl, m are angular momentum quantum numbers withl a positive integer andm an integer such that ml. The rest energy of the particle is ₀, its spin is m, and its lifetime is of the order of 1/. Its antiparticle has ₀ replaced by –₀.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Kinematics of four-wave decay of high-frequency plasma oscillations into upper hybrid and electron-cyclotron plasma waves under multiple electron gyroresonance conditions

We consider the conditions for four-wave decay of two primary plasmons with wave vector and frequency ₀ close to the multiple gyroresonance frequency n_Be into two secondary plasmons with frequencies ₁ > ₀ and ₂ < ₀. The secondary plasmons belong to the upper hybrid and the electron cyclotron branches. It is shown that the main features of the broad upshifted maximum (BUM) in the SEE spectrum can be explained in the context of the proposed process. The BUM feature appears in the region of frequencies having a positive shift from the high-power radio wave frequency. In particular the broad band nature of the BUM can be a result of the broad spectrum of wave number k₀ of the primary plasma waves. In this case the observed cut-off frequency f_cutoff limiting the BUM spectrum on the lower side can result from the lower bound of k₀ (the increase in ₁ corresponds to decay of shorter wave plasmons). In our approach we assume that the generation of primary plasma oscillations by the high-power radio wave and the conversion of secondary plasma waves into the electromagnetic waves is due to coherent scattering of corresponding waves by small-scale magnetic-field-aligned artificial irregularities or to another nonlinear processes.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 3, pp. 301–317, March, 1996.     

Double phase-matched cascaded fifth harmonic generation in single nonlinear medium by focussed laser beam

Generation of a fifth harmonic by the cascading of two phase-matched third-order processes in a single centrosymmetric nonlinear medium with a focused fundamental beam is investigated theoretically. With the help of analytical and numerical investigations the optimized conditions for maximum conversion into the fifth harmonic are found. In general the optimal position of focusing depends on the values of the mismatches k₁ and k₂ for both steps of the third order cascading (++=3; 3++=5). It is shown that for best efficiency this method of fifth harmonic generation requires specially chosen k_1,opt and k_2,opt and focusing in the center of the nonlinear media. If the phase matching parameters are fixed and they deviate from the optimal values, then the optimal strength of focusing and position of the focus spot should be calculated according to the analysis presented here. PACS 42.65.-k; 42.65.Ky; 42.79.Nv     

Dynamical chaos in the highly excited states of a quantum Daffing oscillator in an external harmonic field

The energy spectrum of the highly excited states of a quantum Daffing oscillator is considered. It is shown that the energy levels satisfy E_n>E_n+1 and E_n -F²/8², when n , where F² and are the intensity and frequency of the external field. It is suggested that this property of the spectrum is the quantum manifestation of a stochastic attractor in the classical nonlinear limit. This property also takes place for large F².Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 90–94, March. 1993.     

Possible use of a gas-discharge plasma in an oscillating field to modulate electromagnetic radiation

The conditions for resonance and signal cutoff are determined from the dispersion relation for the complex refractive index for a plane electromagnetic wave propagating in a gas-discharge plasma when a magnetic field H = H₀ + H₁e^jt is imposed on the plasma. The refractive index and absorption are calculated for circularly polarized waves as functions of the alternating magnetic field with _p, _b, andv as parameters. Possible observation of modulation of the transmitted signal is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 94–99, April, 1971.     

Effect of the polarization of the electromagnetic wave on wave energy absorption caused by the linear transformation of waves

The paper deals with the experimental verification of the effect of the polarization of the electromagnetic wave on the linear transformation of waves in an inhomogeneous magnetoactive plasma. Experiments were carried out in magnetic field satisfying condition _ce/>1, where _ce, are the electron cyclotron frequency and the frequency of the electromagnetic wave. The expressive dependence of the electromagnetic wave energy absorption on its polarization found experimentally is in excellent agreement with the theory.The authors wish to thank the director of the Institute of Plasma Physics Dr. J. Váa for his interest in this work and to Drs. R. Klíma, V. Kopecký and J. atlov for many valuable discussions and comments.     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Low frequency limits of third-order harmonic coefficients for atomic hydrogen in any level of discrete energy spectrum

In this paper the analytical expression is derived for the third-order optical harmonic coefficients x _abcd ^v (,,) of the atomic hydrogen at very low frequencies 0 in many level of the discrete energy spectrum.The author expresses his thank to Prof. Nguyen Van Hieu for suggesting the problem and fruitful discussions.     

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.     

Systematic perturbation calculation for a non commutative model for a metallic glas

We present a systematic perturbation calculation up to the 4th order in the interaction for a metallic-glas-model with an anisotropic coupling of the conduction electrons to a local two-level-system. The logarithmic-(infrared-)divergent terms for the electronic lifetime are suppressed by exponentially small prefactors in the region I (ET) whereas in the region II (ET) they survive in the general case of non-commuting elastic and inelastic couplings in the Hamiltonian, whereE denotes the level-splittings of the local-system, the excitation energy of the conduction electrons above the Fermi level, andT the thermal energy.     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of d-dimensional Anderson models on l²( $$\mathbb(z)$$^d) defined by the product U=D S where S is a deterministic unitary and D is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of U(U –z)^–1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for U.     

Some exact models for nonspherical collapse. III

The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x ²,x ³) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x ²,x ³) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

A theory of the weakly pinned Fröhlich mode

Extending earlier work of Littlewood (1987) a theory for the collective mode (Fröhlich mode) response of weakly pinned charge density waves (CDW) is given. Long range Coulomb interaction is incorporated in both a proper definition of the measured ac conductivity _CDW() and in the Fukuyama-Lee-Rice treatment of phason dynamics. The frequency and wave number dependent quasi particle resistivity is shown to appear only in the internal phason lines in the perturbation expansion of the impurity averaged phason propagatorD _ren. Quantitative results for _CDW() are evaluated within the self-consistent Born approximation toD _ren in three spatial dimensions taking anisotropy into account. Besides the low frequency relaxation mode we find a significant effect of the longitudinal optical phason _LO on the Fröhlich mode pinning frequency when descreening sets in at low temperatures. This is yet another manifestation of selection rule breaking by inhomogeneous pinning and establishes the special role that _LO plays in the dynamics of CDW. An explicit analytical formula for _CDW() is given and discussed in some detail including the important analyticity properties. Available measurements of the linear ac response in a wide range of frequencies and conductivities are compared with the theory and found to agree with the theoretical predictions supporting the concept of weak pinning in CDW.