Vibrational anomalies and marginal stability of glasses

The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye’s elasticity theory: The density of states deviates from Debye’s ω² law (“boson peak”), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω^1+a is predicted with a ? 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation.     

A theoretical study of operation conditions for a terahertz superlattice parametric oscillator

We report a theoretical study of operation conditions for a terahertz superlattice parametric oscillator (SPO). The SPO converts radiation of frequency ω to radiation at frequency 3ω. The parametric process is based on the nonlinearity of the motion of a miniband electron in a high-frequency field consisting of a strong fundamental-frequency field and a higher harmonic field. In our study we made use of a semiclassical theory. Our analysis indicates that parametric frequency upconversion should allow for production of radiation up to several terahertz.     

Subsonic flapping flutter

A mathematical model of two-dimensional flow through a flexible channel is analyzed for its stability characteristics. Linear theory shows that fluid viscosity, modelled by a Darcy friction factor, induces flutter instability when the dimensionsless fluid speed, S, attains a critical flutter speed, S₀. This is in qualitative agreement with experimental results, and it is at variance with previous analytical studies where fluid viscosity was neglected and divergence instability was predicted. The critical flutter speed and the associated critical flutter frequency depend on three other dimensionless parameters: the ratio of fluid to wall damping; the ratio of wall to fluid mass; and the ratio of wall bending resistance to elastance. Non-linear theory predicts stable, finite amplitude flutter for S>S₀, which increases in frequency and amplitude as S increases. Both symmetric and antisymmetric modes of deformation are discussed.     

Zero frequency dynamical structure factor of liquids

Expressions for the zero frequency dynamical structure factor, S(k, ω = 0), are derived from the theory of collective motion of liquids proposed by the authors and that by Hubbard and Beeby. Calculations on liquid argon show that in comparison with the latter, the former theory gives much higher values of S(k, 0) which are in good agreement with the recent experimental results.     

Evaluation of the dipole interaction of a pair of metal particles in the region of the plasmon resonance

We consider the electric field of an induced dipole moment of a single small particle characterized by the absence of frequency dispersion of the permittivity and the field of a metal particle, which has frequency dispersion and is described in the free electron approximation taking into account the size effects of restriction of the electron free path. The influence of the induced field on the optical properties of a system of small particles is analyzed. It is shown that, for an ensemble of particles without frequency dispersion, the effective medium theory can be used up to concentrations corresponding to filling factors ? ≤ 0.52. In the case of metal particles, with frequency dispersion of dielectric functions and, especially, for the frequency range of the plasmon resonance, this theory can be used only for concentrations not exceeding the threshold ? ≈ 0.01.     

Application to Rat Lung of the Extended Rorschach–Hazlewood Model of Spin–Lattice Relaxation

The spin–lattice relaxation timeT₁was measured in excised degassed (airless) rat lungs over the frequency range 6.7 to 80.5 MHz. The observed frequency dependence was fitted successfully to the water–biopolymer cross-relaxation theory proposed by H. E. Rorschach and C. F. Hazlewood (RH) [J. Magn. Reson.70,79 (1986)]. The rotating frame spin–lattice relaxation timeT_1ρwas also measured in rat lung fragments over the frequency range 0.56 to 5.6 kHz, and the observed frequency dependence was explained with an extension of the RH model. The agreement between the theory and the experimental data in both cases is good.     

Hydrogen maser frequency shifts due to coherently excited Δm F =±1 transitions betweenF=1 levels of the atomic hydrogen ground state

Hydrogen maser frequency shifts, caused by the multiple quantum transition nonlinearities of a resonant multiple frequency excitation of the atomic hydrogen four level ground state system have been investigated. The oscillation characteristics of hydrogen maser operation with simultaneously excited, low frequencyΔm _F =±1 transitions between theF=1 states of the atomic hydrogen ground state have been analysed theoretically and explicit formulas for hydrogen maser frequency shifts and amplitude response have been derived for arbitrary maser oscillation amplitude and a small signal approximation for theΔm _F =±1 “Zeeman” transitions. The comparison with experimentally observed hydrogen maser frequency shifts was specialized to small magnetic fields, for which the difference between the resonance frequencies of the two low frequency,Δm _F =±1 Zeeman transitions is small compared to the linewidth. Special emphasis was placed on the evaluation of frequency pulling effects for a Zeeman transition excitation at off-resonance conditions. For this case the theoretical formulation of frequency pulling effects becomes insensitive against simplifying assumptions about the radiation damping phenomena and a particular good agreement between experiment and theory can therefore be expected. Experimental conditions have been specified, for which the uncertainty of hydrogen maser frequency due to Zeeman transition induced frequency shifts does not restrict the present frequency stability of a hydrogen maser frequency standard.     

Interaction of a laser with a qubit in thermal motion and its application to robust and efficient readout

We present a detailed theoretical and experimental study on the optical control of a trapped-ion qubit subject to thermally induced fluctuations of the Rabi frequency. The coupling fluctuations are caused by thermal excitation on three harmonic oscillator modes. We develop an effective Maxwell–Boltzmann theory which leads to a replacement of several quantized oscillator modes by an effective continuous probability distribution function for the Rabi frequency. The model is experimentally verified for driving the quadrupole transition with resonant square pulses. This allows for the determination of the ion temperature with an accuracy of better than 2% of the temperature pertaining to the Doppler cooling limit T _D over a range from 0.5T _D to 5T _D . The theory is then applied successfully to model experimental data for rapid adiabatic passage (RAP) pulses. We apply the model and the obtained experimental parameters to elucidate the robustness and efficiency of the RAP process by means of numerical simulations.     

On the nature of a lattice vibrational mode at a frequency of 135 cm−1 in Hg1 − x Cd x Te alloys

The vibrational spectrum of a cadmium impurity atom in the HgTe crystal has been calculated using the microscopic theory of lattice dynamics in the approximation of a low impurity concentration. Within this theory, the behavior of the local and quasi-local modes induced upon substitution of the lighter Cd atom for the Hg atom in the region of the zero or very low one-phonon density of states in the HgTe crystal has been considered. It has been found that, apart from the local mode at a frequency of 155 cm^?1, the calculated vibrational spectra exhibit a weak (but clearly pronounced) feature at a frequency of 134 cm^?1, which coincides with the experimentally observed vibrational mode (the “minicluster” mode) at a frequency of 135 cm^?1 in the Hg_{1 ? x} Cd _x Te (x = 0.2–0.3) alloys at 80 K.     

A phenomenological theory of light scattering by surfaces: II. Rough surfaces

The theory developed in a previous paper is applied to the special case of rough surfaces. An existing controversy is discussed and resolved within the context of our theory. Formulae for the frequency dispersion of the scattered light due to motion of the interface are also given which makes the theory applicable to e.g. a fluid-fluid interface.     

Optical conductivity of a two-band superconductor

Within the two-band superconductor model, which is a generalization of the standard BCS model to the case of a complicated crystal structure, an expression has been obtained for the conductivity of the superconductor at an arbitrary frequency of the external electromagnetic field. This expression has been derived using the microscopic theory in the framework of the diagram technique for nonequilibrium processes. The σ(ω) dependencies calculated for T = 0 are compared with the results of single-band models with the s and d symmetries of the order parameter. It has been shown that the behavior of the optical conductivity as a function of the frequency depends strongly on the doping level.     

Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity

By employing a simplified nonlinear coupled mode theory, we discuss the influence of two-photon absorption (TPA) on the characteristics of bistable switching. It is revealed that the critical value of frequency detuning for bistability rises linearly with increasing TPA coefficient k (when k is less than 30), and eventually access to a saturated value. It is also found that TPA effect will be enhanced for a greater frequency detuning, especially when transmission reaches its peak value. As a result, the peak transmission will decrease monotonously with the increasing frequency detuning. Based on this simplified model, the TPA-induced temperature rise in microcavity is also estimated. The theoretical predictions show good agreement with the simultaneous results, as well as the proposed experimental phenomena.     

Rayleigh wave dispersion and attenuation on a statistically rough free surface of a hexagonal crystal

Dispersion and attenuation of Rayleigh surface acoustic waves on a statistically rough free surface of a Z-cut hexagonal crystal were analytically studied using a modified mean-field method within the perturbation theory. Numerical calculations were carried out in the frequency range accessible for the perturbation theory using expressions for the real and imaginary parts of the complex frequency shift of Rayleigh waves caused by a slight surface roughness. The Rayleigh wave dispersion and attenuation in the Z-cut hexagonal crystal were shown to coincide qualitatively with those in an isotropic medium, differing only quantitatively. In the long-wavelength limit λ?a, where a is the lateral roughness correlation length, explicit analytical expressions for the relative change in the phase velocity and the inverse damping depth of Rayleigh waves were derived and used in numerical calculations.     

The self-consistent determination of HF electroconductivity of strongly coupled plasmas

Here is presented the calculation of the dynamic electrical conductivity of fully ionized, strongly coupled plasmas as a function of the external electric field frequency ω. The calculations are based on the formula for the energy-dependent collision frequency which is determined by means of the Green function theory methods, as a sum over the Matsubara frequencies. The domain of extremely high electron density: ¹⁰²¹?ne?¹⁰²⁴ cm−3, and for the temperature varying from 10 kK to 1000 kK was examined. The real and imaginary parts of the conductivity for every electron density are presented in the generalized Drude-like form as a two-parameter function of the frequency ω in the region 0<ω<0.5ωp, where ωp is the plasma frequency. A good agreement between the obtained results and the existing theoretical and computing simulation data is shown.     

Improved broad bandwidth intersections in photonic crystals

We theoretically investigate the transmission properties of a cascade of cavities coupled to waveguide by the time domain coupled-mode theory. Based on the theoretical analysis, broad bandwidth optical waveguide intersections in photonic crystals are modeled and optimized. The transmission properties are simulated by finite-difference time-domain method and transmission coefficients higher than 98% for a wide frequency range between 0.360 (2πc/a) and 0.364 (2πc/a) are obtained.     

An anisotropic model for frequency analysis of arterial walls with the wave propagation approach

An anisotropic model for calculating natural frequency of arterial walls is proposed in this paper. The first-order shear deformation theory (FSDT) is used for the arterial walls, and the wave propagation approach is applied that can easily handle the boundary conditions. Results obtained using this model have been evaluated against those available in the literature and the agreement has been found to be good. Experiments were carried out on a natural rubber latex tube. The relative differences of the first four natural frequencies between the experiment and the theory are less than 7%. The variation of the natural frequency of this tube with the longitudinal and circumferential modes m and n is studied which suggests the first four natural frequencies are with n = 1 and m = 1-4. Simulations show that classical Donnell’s, Love’s and beam theories are not suitable for this thick tube while FSDT results closely agree with the experiment. The anisotropy of circumferential elastic modulus on natural frequencies of the tube is analyzed.     

Development of stochastic webs in a wave-driven linear oscillator

We present developments of stochastic webs in a linear oscillator which is driven by a finite number (N) of external waves with frequency ω₀ (harmonic of the linear oscillator frequency). The expansion of the stochastic domain as functions of the number of waves and their amplitudes is studies numerically. The results with small amplitude waves compares well with the perturbation theory. When the amplitude of external waves is small a leaf structure which expands with N develops radially in the phase space.     

Estimation of Critical Point in Branching Reactions: Further Examination of Gel Point Formula

The theory of gel point in real polymer solutions is examined with the empirical correlation between the reciprocal of the percolation threshold and the coordination number given by the percolation theory. Applying a larger value of the relative frequency of cyclization, an excellent agreement is obtained between the present theory and the percolation result. This suggest that while the ring distribution on lattices is similar to that in real systems, ring production is more frequent in the lattice model than in real systems. To confirm this conjecture, we derive the ring distribution function of the lattice model as a limiting case of d→∞, and show that the solution is in fact identical to the asymptotic formula of C→∞ in real systems except for the coefficient C, which has a maximum at d = 5, in support of the above conjecture. To examine the validity of the asymptotic solution for the lattice model, we apply it to the critical point problem of the percolation theory, showing that the solution works well in high dimensions greater than six.