Spectra of Hamiltonians with generalized single-site dynamical disorder

Starting from the deformed commutation relationsa _q (t) a ^q (s)–q a ^q (s) a _q (t)=(t–s)1, –1q1 with a covariance (t–s) and a parameterq varying between –1 and 1, a stochastic process is constructed which continuously deforms the classical Gaussian and classical compound Poisson process. The moments of these distinguished stochastic processes are identified with the Hilbert space vacuum expectation values of products of with fixed parametersq, and . Thereby we can interpolate between dichotomic, random matrix and classical Gaussian and compound Poisson processes. The spectra of Hamiltonians with single-site dynamical disorder are calculated for an exponential covariance (coloured noise) by means of the time convolution generalized master equation formalism (TC-GME) and the partial cumulants technique. The final result for the spectral function is given as aq-dependent infinite continued fraction. In the case of the random matrix processes the infinite continued fraction can be summed up yielding a self-consistent equation for the one-particle Green function.     

Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system

A two-mode saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise is considered. The laser intensity Langevin equation and corresponding Fokker-Planck equation are derived by the phase-locking method. The effects of the cross-correlation strength λ between the real and imaginary parts of quantum noise and the cavity decay constant K on the steady-state intensity distribution Q(I₁,I₂), the mean light intensity 〈I〉, the normalization autocorrelation λ₁₁(0) and cross correlation λ₁₂(0) are studied by numerical calculation. The results show that as λ increases the Qs(I₁,I₂) show two extrema, and λ almost does not affect the 〈I〉, λ₁₁(0) and λ₁₂(0) when the laser system is operated far above threshold. Nevertheless, when the laser system is operated at and below threshold, λ makes the curves of Qs(I₁,I₂) have the higher peak and drop faster. Furthermore, it enhances the deviation of λ₁₁(0) and λ₁₂(0) and lessens the mean light intensity 〈I〉 when the laser system is operated at and below threshold.     

Diffusion and correlation in a coherent representation

Using a Fock-space formalism for the Master equation and introducing the density operator we present an unified method to derive kinetic equations for hopping processes with and without exclusion on a lattice. The corresponding Liouvillians are written in terms of Fermi or Bose operators, respectively. Although the Liouvillians are different the averaged particle numbers obey the same diffusion equation. Differences appear in the correlation functions only. The Master equation can be transformed into a differential equation in a coherent state representation. Using the algebraic properties of Grassmann numbers we are able to find the exact statonary solution for diffusion with exclusion. The conductivity can be derived in the bosonic and the fermionic case. The results are in accordance with those obtained with different other methods.     

Four-photon processes stimulated by a fluctuating pump

Four-photon parametric light amplification stimulated by noisy pump in a dispersive medium, is theoretically analyzed. The model of the fluctuating phase is used. The increments in case of temporal as well as of spatial laser pump modulation are considered. It is shown that the efficiency of the four-photon process due to a broad-band pump is comparable to that of monochromatic pump. Quantitative estimates for the medium of metal vapor are given, too.     

Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems

Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems.     

Negative-ion emission during laser ablation of multicomponent materials

The time of flight technique coupled with an electrostatic energy filter has been used for composition and energy-distribution analysis of the ion species emitted during laser ablation of multicomponent materials Y-Ba-Cu-O, Pb-Sn-Te. The negative-ion output and kinetic-energy distribution as a function of the laser wavelength and the laser fluence on the target were measured. A high output of the negative ions of matrix elements comparable with the positive-ion emission was detected. The barium negative-ion formation was observed in spite of the negative electron affinity of alkaline earth elements in the ground electronic state. The mechanism of negative-ion formation based on the ternary collisional recombination in the laser plasma is analyzed.     

A study of blast waveforms detected simultaneously by a microphone and a laser probe during laser ablation

We examine blast waves generated in air during irradiation of absorbing samples with Nd: YAG laser pulses of fluences exceeding the ablation threshold. Blast waves were detected simultaneously by a wideband microphone and a laser beam deflection probe. By a comparative analysis of both signals in the time and frequency domain we investigate characteristic features of their nonlinear waveform evolution. To explain the observed phenomena we employ the weak shock solution of the point explosion model.     

Effects of dynamic response time in an evolving market

Considering the time scales of global information and personal reaction, we study the role of dynamic response time in the evolution of collective behavior in an evolving market. The insensitiveness to the market information makes the population cluster around a kind of extreme behavior, in which they always follow what happened last time, while a sensitive population tends to self-segregate into opposing groups. The average success rate R among all the agents is found to have a nonmonotonic dependence on the time scale parameter q. There exists a critical value below (above) which R decreases (increases) with the rise of q. Theoretical analyses demonstrate that the higher efficiency found in the market with an insensitive population is related to its predictability. In such a predictable market, the agents following current prediction have a higher winning probability than those rejecting it. Analytical calculations are in good agreement with numerical data.     

Two unstable oscillations in the multimode laser with modulated inversion

We present comprehensive results of numerical studies on the dynamical properties of a multimode ring laser under modulation of the population inversion in the bad-cavity condition. Incoherent properties of unstable oscillations in this system are investigated in detail as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. Two kinds of optical chaos in two limiting regions reported in a previous paper are extensively studied to clarify their different characteristics from deterministic and stochastic points of view. The competition between their different origins is revealed. Statistical properties of their stochasticity are investigated to clarify their non-Gaussian natures. Comparison with analytical results for a single-mode laser with fluctuations is also made.     

Thermal deformation of a solid surface under laser irradiation

A calculation is presented for the deformation of a solid surface when subjected to laser irradiation. The elastic response of the target is given in terms of the stress and displacement field due to thermal expansion, thus allowing an explicit evaluation of the shape of the deformed target surface. Quantitative results are obtained for the height and shape of the induced bump as a function of the laser pulse and target properties. The thermal load threshold is specified for the onset of plastic yield.     

Field-emission flicker noise from potassium adsorbed on W(111) bounded and unbounded surface diffusion by spectral analysis

The spectral density functionsW(f) of the field-emission flicker noise of potassium adsorbed on the tungsten (111) region were determined. The analysis in terms of the Gesley-Swanson or the Timm and Van der Ziel model gives surface diffusion energies between 0.54 and 0.31 eV for (average) coverages from 0.15 to 0.38 and diffusion prefactors between 3×10^–1 and 10^–4 cm²/s. The fitting procedures are successful for both bounded and unbounded diffusion though in opposite order of temperature, as expected.On leave from Wrocaw University     

Stochastic diagrams for critical point spectra

A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an N-dimensional phase-space. These serve as a useful paradigm for describing critical point phase transitions in numerous equilibrium and non-equilibrium systems, ranging from chemistry, physics and biology, to engineering, sociology and economics. The technique consists in developing the stochastic variable as a power series in time, and using this to compute the short time expansion for the correlation functions. This is then extrapolated to large times, and Fourier transformed to obtain the spectrum. Stochastic diagrams are developed to facilitate computation of the coefficients of the relevant power series expansion. Two different types of long-time extrapolation technique, involving either simple exponentials or logarithmic rational approximations, are evaluated for third-order diagrams. The analytical results thus obtained are compared with numerical simulations, together with exact results available in special cases. The agreement is found to be excellent up to and including the neighborhood of the critical point. Exponential extrapolation works especially well even above the critical point at large N values, where the dynamics is one of phase-diffusion in the presence of a spontaneously broken symmetry. This method also enables the calculation of the steady state spectra of polynomial functions of the stochastic variables. In these cases, the final correlations can be non-bistable even above threshold. Here logarithmic rational extrapolation has the greater accuracy of the two extrapolation methods. Stochastic diagrams are also applicable to more general problems involving spatial variation, in addition to temporal variation. Received: 12 January 1998     

Protein conformational fluctuations and free-energy transduction

Non-equilibrium fluctuations, whether imposed externally or driven by an energy-releasing chemical reaction, can cause a protein to cycle through several conformations. This cycling can drive a process thermodynamically uphill even though any one conformation considered independently catalyzes the process in the downhill direction. This is because the different conformations have different rate constants (energy barriers) between the states in the catalytic cycle. Even though each conformation individually obeys detailed balance, the flashing between different energy profiles gives rise to a ratchet effect. Further, by exploiting protein conformational dynamics, a single stochastic input can be converted into two phase-shifted internal parameters (e.g. a kinetic barrier height and a binding well energy). This allows the output process to be driven nearly adiabatically, explaining in part the very high efficiencies observed for some biological energy-transduction processes. The results apply equally to driving a biochemical reaction away from equilibrium by an enzyme, to formation of an osmotic gradient across a membrane by a molecular pump, or to motion and generation of force by a molecular motor. Received: 8 February 2002 / Accepted: 4 March 2002 / Published online: 22 April 2002     

Statistical properties of thermal radiation in a Kerr nonlinear blackbody

We study the statistical properties of thermal radiation in a Kerr nonlinear blackbody in which bare photons with opposite wave vectors and helities are bound into pairs and unpaired photons are transformed into a different kind of quasiparticle, the nonpolariton. This paper investigates the statistical properties of the photon blackbody field by using the second-order correlation function, the phase space distribution function, the photon number distribution and the nonclassical depth. The numerical computation and a discussion of the results are present.     

Abnormal properties of spontaneous emission in a Kerr nonlinear blackbody

We reexamine the atomic spontaneous decay in a Kerr nonlinear blackbody by contrast with our previous paper [M. Yin, Z. Cheng, Phys. Rev. A 78 (2008) 063829]. In the process of deriving the atomic decay rate, we use the temperature-dependent velocity of photons to take the full nonlinearity of a KNB into account. It is found that below a transition temperature T_c, the atomic spontaneous emission in a KNB might be enhanced or inhibited compared with that in a normal blackbody whose interior is filled with a nonabsorbing linear medium. The physical origin of the enhancement and inhibition of spontaneous emission is also discussed.     

Some results for a fractional diffusion equation with radial symmetry in a confined region

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e.,  with . The equation is considered in a confined region and subjected to time dependent boundary conditions which may be related to inhomogeneous characteristics of the surfaces confining the system. The results show an anomalous spreading of the solutions and an unusual behavior of the survival probability.     

Temperature distribution in a film heated with a laser spot: Theory and measurement

For the measurement of the thermal capacity and the thermal conductivity of films, the thermal excitation of the sample is commonly performed by the absorption of light. This results in a spatial and temporal temperature distribution within the film. With a variety of methods static or dynamic temperature recordings are performed.Two problems with these methods are discussed, the calculation of the temperature distribution in the film and the measurement of the mean surface temperature of the film. An analytical solution of the heat conduction problem for a cylindrical geometry with any radial distribution of the absorbed light is given. Resistive bolometers are introduced for the measurement of the mean surface temperature of the film within a circular area. Experiments with a 25 m thick PVDF film give excellent agreement with the theoretical calculations within the modulation frequency range 10^–3 Hz to 10³ Hz, thus allowing a determination of various thermal parameters of the investigated film.     

Finite-size-induced transition in ensemble of globally coupled oscillators

The collective behavior of overdamped nonlinear noise-driven oscillators coupled via mean field is investigated numerically. When a coupling constant is increased, a transition in the dynamics of the mean field is observed. This transition scales with the number of oscillators and disappears when this number tends to infinity. Analytical arguments explaining the observed scaling are presented.     

High-resolution nonlinear laser spectroscopy of exciton relaxation in GaAs quantum wells

This paper describes measurements of exciton relaxation in GaAs/AlGaAs quantum well structures based on high resolution nonlinear laser spectroscopy. The nonlinear optical measurements show that low energy excitons can be localized by monolayer disorder of the quantum well interface. We show that these excitons migrate between localization sites by phonon assisted migration, leading to spectral diffusion of the excitons. The frequency domain measurements give a direct measure of the quasi-equilibrium exciton spectral redistribution due to exciton energy relaxation, and the temperature dependence of the measured migration rates confirms recent theoretical predictions. The observed line shapes are interpreted based on solutions we obtain to modified Bloch equations which include the effects of spectral diffusion.     

Exact solutions for a forced Burgers equation with a linear external force

We investigate the solutions of the Burgers equation , where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k₁(t)−k₂(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k₁(t) and k₂(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ₁(t)+Φ₂(t)x and Φ(x,t)=Φ₃x−Φ₄/x³ are incorporated in the previous analysis and exact solutions are obtained for both cases.