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.     

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.     

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.     

Tunable UV radiation at short wavelengths (188–240 nm) generated by sum-frequency mixing in lithium borate

Sum-frequency mixing (₃=₁+₂) of UV laser radiation (₁=266 nm and 213 nm) and tunable coherent infrared light (₂=1.2–2.6 m) in lithium borate (LBO) generates radiation at short wavelengths (₃=188–242 nm). The UV radiation at ₁ is produced by the fourth and fifth harmonic of a pulsed Nd-YAG laser. The infrared light is generated with an optical parametric oscillator of beta barium borate. The phase-matching angle is measured as function of ₃ and compared with calculated values. For UV laser radiation at shorter wavelengths (173 nm₁213 nm) the calculations predict an extension of the tuning range of the sum-frequency generated at ₃ to wavelengths as short as the LBO transmission cutoff at 160 nm.     

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.     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.     

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.     

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.     

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.     

Second-harmonic generated by self-squeezed light in isotropic medium. The role of light intensity-dependent effects and molecular-statistical structure

An isotropic medium with electrically removed centre of symmetry in which a fundamental wave at frequency generates the second harmonic at 2 is considered. The two waves give rise to self-acting effects modifying the refractive indices at and/or 2 (selfinduced ellipse rotation, optical Kerr effect). For this physical situation, an effective interaction Hamiltonian is introduced involving nonlinear coupling parameters, discussed versus the dc electric field and temperature as well as the density, concentration and molecular structure of the medium. The solutions of the respective quantum equations for the field operators at and 2 permit, in particular, the calculation of the variances for a novel process of second-harmonic generation by light, self-squeezed in an isotropic medium. It is shown that squeezing in the out-of-phase component of the second harmonic beam follows, with some delay, after self-squeezing in the in-phase component of the fundamental beam.Sponsored by the Polish Academy of Sciences, Project CPBP 01.12     

Recursion method for the density of states and spectral dimension of central-force elastic percolation network

We use the recursion method to calculate the vibrational density of states () of site diluted central-force elastic percolation network on the triangular lattice. We find that () is proportional to at long wavelengths. At shorter wavelengths, i.e. in the fracton regime, () is proportional to , where is the spectral dimension of the elastic percolation network. A log-log plot of () vs gives a straight line in the fracton regime with a negative slope. From this we estimate {ie333-3} to be 0.625.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

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.     

Subharmonic electromagnetic radiation from cavitons

In a high-power microwave-plasma system, it has been experimentally found that electromagnetic (em) radiation at subharmonic frequencies [specifically, (3/2)₀ and (5/2)₀] of the electron plasma frequency of the unperturbed state, ₀, can be emanated from cavitons which are resonantly driven by an intense em pulse (frequency ₀) in an unmagnetized inhomogeneous plasma. Electron oscillations at ~ (1/2)₀ are preferentially excited inside a deep (|n/n_c|0.5) caviton although this is not deep enough to resonantly support (1/2)₀ oscillations. The experimental results show that the coupling between the (1/2)₀ electron oscillations inside the caviton and the electron plasma waves at (3/2)₀, which is originally excited due to the mode conversion of the incident microwave at the resonant layer and which generates the caviton, produces a localized nonlinear current which emits em waves at (3/2)₀. A similar coupling between (3/2)₀ and ₀ frequencies can emit em waves at (5/2)₀. The model to explain the above new phenomenon is discussed.Institute of Research and Development, and School of High Technology for Human Welfare, Tokai University, Japan. Department of Physics, University of California, Los Angeles, California. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 5, pp. 596–616, May, 1994.     

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)}.     

The third-order electric susceptibilities of NaCl and KCl monocrystals

The dispersion of the third-order electric susceptibilities(; , , –) and(; , 0, 0) of NaCl and KCl monocrystals has been calculated by means of experimental data on the electro-optic Kerr effect. The result has been obtained by using semi-classical models of anharmonic oscillators. An ionic contribution to the electro-optic coefficients has been presented. From the result obtained it follows that the third-order electric susceptibilities are of the order of 10^–22 m² V^–2.     

Parametrizing Equivalence Classes of Invariant Star Products

Let (M,,) be a symplectic manifold endowed with a symplectic connection . Let Symp(M,) be the group of symplectic transformations of (M,) and Aff(M,) be the group of affine transformations of the affine manifold (M, ). In this Letter, we show that, for any subgroup G of Symp(M,) Aff(M,), the set of G-equivalence classes of G-invariant star products on (M,) is canonically parametrized by the set of sequences of elements belonging to the second de Rham cohomology space of the G-invariant de Rham complex on M.     

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.     

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.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.