Nonlinear Raman scattering of photons by a channeled particle

Channeled particles are characterized by the discrete spectrum of bound transverse motion. The interaction of photons with channeled particles in single crystals can be accompanied by energy transitions between the levels of transverse motion of the channeled particle. The Raman scattering of photons at a quasibound channeled particle leads to the appearance of a combination of frequencies: the incident radiation frequency ω₀ and the frequency Δω_{m, n}, i.e., ω = ω₀ ± Δω_m,n where Δω_m,n = 2Δε_m,nγ²; Δε_{m, n} is the energy of the transition between quantum states (m and n) of the transverse motion of the channeled particle; and γ = E/mc² is the Lorentz factor of the channeled particle. The appearance of a violet satellite (the anti-Stokes component) in the Raman scattering spectrum is analyzed. The three-photon Raman-type transition, which is the process of the simultaneous absorption of two photons with the frequency ω₀ with the emission of a photon with the frequency ωs = 2ω₀ ± 2Δε_m,nγ², is considered. The conditions for resonance observation during the formation of the second harmonic (ω = 2ω₀) are discussed.     

Nonlinear susceptibilities of vapors and solutions of organic dyes

Results of theoretical studies of laser and Kerr nonlinear susceptibilities of vapors and solutions of organic dyes using a series of polycyclic arenes as an example are presented. Nonlinear susceptibilities of the third χ⁽³⁾ (?3ω; ω, ω, ω) and the fifth χ⁽⁵⁾ (?3ω; ω, ω, ω, ω, ?ω) orders of a series of organic dyes responsible for third harmonic generation of Nd:YAG laser radiation are calculated within the context of the free electron model. Results of calculations of their Kerr third-order nonlinear susceptibilities χ⁽³⁾ (?ω; ω, ?ω, ω) and non-linear refractive indices n ₂ are presented. The calculation results are compared with experimental data on third harmonic generation in naphthalene vapors and with χ⁽³⁾ (?ω; ω, ?ω, ω) as well as n ₂ of paraterphenyl and naphthalene solutions.     

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_rf is close to the Rabi frequency ω₁ in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ? are accompanied by higher-frequency oscillations at frequencies nω_rf and nω_rf ± ?, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ? on the sign of the detuning ω₁ ? ω_rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_rf + ? increases, while the amplitude at the difference frequency ω_rf ? ? decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′₁ centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.     

Lattice self-diffusion in plastic pivalic acid (acid 2.2 dimethyl propanoic)—III: Computer calculation of the correlation factor for various tracer self diffusion mechanisms. Discussion of these mechanisms

The correlation factors ? for lattice self-diffusion of tracers involving mono or divacancies have been calculated in “plastic” pivalic acid. The peculiarities of the crystalline structure have been taken into account. Dimers (molecules linked by 2 hydrogen bondings) induce short range order, but no long range order. The local order changes at the frequency ω_R with which hydrogen bondings break. ? has been obtained using the encounter model and the Monte Carlo method. It has been supposed that hydrogen bondings never break during an encounter. The calculation gives the upper limit of ? for ω_m = nω_R, where n ? 2 and ω_m is the frequency of migration of the defect. The asymptotic value of ? for n→∞ is also obtained. Two diffusion mechanisms for monovacancies as well as for divacancies have been considered. All these mechanisms are strongly correlated. In every case, dimers induce low values of ?. Other experimental data concerning point defects and diffusion in pivalic acid are discussed. Lattice self-diffusion should be due mainly to relaxed monovacancies migrating according to mechanism 1 (exchange of the monovacancy with one of the two molecules forming a dimer). This mechanism is characterised by 0.38 ? ? ? 0.57. Some contribution of divacancies, noticeable above 301K, is not incompatible with experimental data in the whole plastic range.     

The resonance interaction of vibrational modes in one-dimensional nonlinear lattices

Resonances of vibrational modes were for the first time revealed for the example of the one-dimensional random Morse lattice. The observation of resonances was possible because of lattice deformation, when, at certain relative deformation values, vibrational modes satisfied the conditions of double (m _i ω _i + m _j ω _j = 0) or triple (m _i ω _i + m _j ω _j + m _k ω _k = 0) resonances. Of all the resonances observed, the resonance with the frequency ratio ω₂: ω₁ = 2: 1 was studied in detail. The dependences of mode lifetimes and the degree of energy exchange between them on such parameters as resonance frequency detuning, excitation energy level, etc. were determined. A model of two nonlinearly coupled harmonic oscillators was considered in detail on the assumption of a one-to-one correspondence between oscillators and vibrational modes. A consideration of the model problem of oscillators revealed analytic dependences of the dynamic behavior of vibrational modes on control parameters. Excellent agreement between the numerical results for the Morse lattice and analytic conclusions was obtained. It was shown that, for the Fermi-Pasta-Ulam lattice, the resonance interaction of vibrational modes was controlled by the same rules as with the Morse lattice.     

高频引力波对环形波导中电磁波的调制作用

讨论了垂直入射的、频率为ω_g的平面高频引力波对环形波导管中频率为ω_e的电磁波的调制作用．一般情况下，在波导管中与引力波传播方向垂直的对称平面附近，电磁波的能流密度会出现三种新的频率成分（2ω_e±ω_g）和ω_g．在ω_g》ω_e时，能流密度振幅的相对调制量与引力波的无量纲振幅h₀数量级相同．特别是当ω_g，ω_e和电磁波绕波导传播的绕行频率ω₀满足关系ω_g＝2ω_e》ω₀时，由于类似于共振的机制，能流密度会出现比h₀大几个数量级的振幅相对调制量．这个结果不会由于参数的微小改变而消失，这对于探测极微弱的引力辐射信号将是十分重要的 关键词：     

Impedance and dielectric studies of ferroelectric SrBi2Nb2O9 ceramics

This paper reports the dielectric and impedance characteristics of ferroelectric SrBi₂Nb₂O₉ (SBN) ceramics in the 100 Hz-1 MHz frequency range at various temperatures (300-823 K). A strong low frequency dielectric dispersion (LFDD) associated with an impedance relaxation has been found to exist in these ceramics in the temperature range 573-823 K. The Z″ of the AC complex impedance showed two distinct slopes in the frequency range 100 Hz-1 MHz suggesting the existence of two dispersion mechanisms. This non-ideal behavior has been explained on the basis of the expression, Z*=R₀/(1+(iω/ω₁)^m+(iω/ω₂)ⁿ) [J. Phys. Chem. Solids 53 (1992) 1] where ω₁ and ω₂ characterize the lattice response and the charge carrier behavior, respectively. The exponents m and n were obtained from the curve fitting. The exponent n was found to exhibit a minimum at the Curie temperature, T_c (723 K) whereas the m was temperature independent.     

An YBCO film as a Josephson medium near T c : Frequency and field dependences and scaling relationships

The diamagnetic response of a laser-deposited YBCO film was studied in weak exciting magnetic fields H _ac =H ₀sinωt (H ₀=2–500 mOe, ω/2π=1–30 kHz). An analysis of the experimentally measured diamagnetic response showed evidence of a ring character of the electric field flowing in the sample at small H ₀ values. The plots of T _m (the temperature of maximum dissipative losses χ″₁) versus H ₀ measured at various frequencies showed the existence of a certain critical field strength H*(ω) at which the (1?T _m /T _c ) versus H ₀ ^2/3 plots exhibit a break. A logarithmic dependence of T _m on the frequency ω of the exciting field H _ac is reliably valid only in the region of (ω/2π)>5 kHz. Verification of the scaling relationship showed that this relationship is valid (to within the experimental accuracy) for the frequencies ω above 5 kHz and the field amplitudes H ₀>H*(ω). However, the exponent n in the scaling relationship under consideration is not correlated with the exponent n in the power relationship describing the current-voltage characteristic.     

The turbulence of capillary waves on the surface of liquid hydrogen

It is experimentally demonstrated that the surface excitation of liquid hydrogen at a low frequency results in the turbulent mode in a system of capillary waves. The experimental results are in good agreement with the theory of weak wave turbulence. The pair correlation function of the surface deviations is described by the exponential function ω^m. The exponent m decreases in magnitude from m=?3.7±0.3 to ?2.8±0.2 when the pumping at a single resonant frequency changes to broadband noise excitation. Measurements are made of the dependence of the boundary frequency ω_b of the upper edge of the inertial range in which the Kolmogorov spectrum is formed on the wave amplitude η_p at the pumping frequency. It is demonstrated that the obtained data are well described by a function of the form ω_b∝η _p ^4/3 ω _p ^23/9 .     

Precursors of parametric oscillatory instability in LIGO interferometer

The basis of undesirable effect of parametric oscillatory instability in optical interferometer is provided by excitation of the additional (Stokes) optical mode having frequency ω₁${\omega }_1$, and the mirror elastic mode, having frequency ωm${\omega }_m$. It appears when optical energy stored in the main mode, with frequency ω₀${\omega }_0$, exceeds a certain threshold and the frequencies are related as ω₀?ω₁+ωm${\omega }_0?{\omega }_1+{\omega }_m$. We analyze the time evolution of parametric instability which allows predicting the characteristics of precursors of parametric instability. Observation of such precursors may help avoid parametric instability.     

Influence of the sum frequency on optically pumped parametric amplifiers

Parametric traveling-wave interactions are calculated with the aid of a plane wave approximation, considering the 4 frequencies ω _s , ω _p , ω _I =ω _p ?ω _s and ω _Σ =ω _p +ω _s . Special attention is paid to the case where ω _p ?ω _s . Competition between parametric amplification and upconversion is studied as a function of phase matching and the results are illustrated by means of numerical examples. It is shown that parametric gain disappears if the linear combination of wave vectors, 2k _p-k_I-k_Σ, vanishes. In this situation upconversion with power gain up to about (ω _Σ /ω _s )² is possible. It is concluded that fork _p?k_s the sum frequency ω _Σ can significantly influence parametric forward amplification but does not affect backward wave amplification.     

Evolution of a turbulent cascade on the surface of liquid hydrogen under a change in the spectral characteristic of an exciting force

The modification of the turbulent cascade in a system of capillary waves on the surface of liquid hydrogen under a change in the spectral width of exciting noise has been experimentally studied. The correlation function I _ω of the deviations of the surface of liquid hydrogen from equilibrium under broadband excitation is a monotonically decreasing function of frequency. The distribution I _ω in the inertial range is well described by the power function ω^?m with the exponent m close to 17/6. In the presence of narrowband excitation, a chain of peaks appears on the cascade I _ω; the positions of the peaks are described by a power function of frequency with the exponent m = 3.8 ± 0.1.     

Point-contact spectroscopy of electron relaxation mechanisms in semiconductors

The I–V characteristic of a tiny semiconducting channel connecting bulk electrodes is shown to have singularities arising due to phonon emission by hot electrons at energies eV = n?ω₀, where ω₀ is the optical phonon frequency and n = 1, 2, 3,…. The nonlinear part of the I–V curve provides direct information concerning the energy dependence of the elastic-scattering time of charge carriers.     

Surface-plasmon-polariton dispersion of semiconductors with depletion layers

For a sample with plasma frequency varying exponentially from ω_ps at the surface to a larger value ω_pb in the bulk, and moderate damping, we find, contrary to other calculations, that the long wavelength surface plasmon dispersion has a single branch that is reentrant at ω = ω_ps.     

Narrow band current oscillation amplitudes in the stochastic classical model for sliding charge density waves

The first theoretical investigation of the amplitudes of the narrow band current oscillations generated by sliding charge density waves is given using the stochastic classical model with a current noise source. In contrast to the classical model without fluctuations, the power spectrum S(ω) of the current-current correlation function has finite peaks S²_n and non- vanishing line widths Γ_n near ω = nω_osc where ω_osc is the fundamental frequency of the current oscillations. For weak current noise, analytical expressions for s_n and Γ_n are given which agree with the exact numerical treatment of S(ω) using the Fokker-Planck approach. The results are in accord with the observed asymptotic decrease of the fundamental amplitude s₁ with increasing d.c. bias. They also confirm the validity of the weak noise limit for sliding charge density waves.     

Kotani theory for one dimensional stochastic Jacobi matrices

We consider families of operators,H _ω, on ?₂ given by (H _ω u)(n)=u(n+1)+u(n?1)+V _ω(n)u(n), whereV _ω is a stationary bounded ergodic sequence. We prove analogs of Kotani's results, including that for a.e. ω,σ_ac(H _ω) is the essential closure of the set ofE where γ(E) the Lyaponov index, vanishes and the result that ifV _ω is non-deterministic, then σ_ac is empty.     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Theory of transient two-photon resonant up-conversion with non-synchronized excitation

The theory of the two-photon resonant up-conversion process (ω_a + ω_a) + ω_c ? ω_d is developed for short pulse excitation. Prominence is given to the case where the pulse at frequency ω_c is not time-synchronized with the pulse ω_a but travels immediately behind it. Not only is the conversion efficiency thereby maximized, but the associated theoretical simplification enables several analytical formulae to be derived which provide new insight into the mechanism of resonant non- linear interactions. In particular, an expression is derived for the maximum useful energy per unit area of the pulse at ω_c. Exceeding this value is of little or no advantage in the non-synchronized case and is positively detrimental when the a- and c-pulses are coincident. The results are supported by computer solutions.     

Fractional features in radiation-induced oscillations of the magnetoresistance of two-dimensional electron systems

The magnetoresistance of two-dimensional electron systems irradiated by microwave radiation is calculated. It exhibits oscillatory features at fractional values of the ratio ω/ω_c of the circular frequency of microwave radiation to the cyclotron frequency. The calculation explains existing experimental data by nonequilibrium population of electron states that appears due to one-photon processes and predicts ω/ω_c values near which the basic features in magnetoresistance are expected. In the framework of the mechanism under consideration, the fractional features can be observed only in the crossover from strongly overlapping to separate Landau levels and only at radiation frequencies below the threshold frequencies depending on a fractional value.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.