Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach

Inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged massive Brownian particle model using a path integral approach. We calculate the work distribution function in the laboratory and comoving frames and prove the asymptotic fluctuation theorem for these works for any initial condition. Important and observable differences between the work fluctuations in the two frames appear for finite times and are discussed concretely for a nonequilibrium steady state initial condition. We also show that for finite times a time oscillatory behavior appears in the work distribution function for masses larger than a nonzero critical value.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

On the effect of a magnetic field on fast charged particles passing through a substance

A transport equation in the small-angle approximation is obtained for a curvilinear beam of fast charged particles passing through a substance in a nonuniform magnetic field. Green functions for this equation are found for an annular beam in a weak-focusing field and for a helical beam in the nonuniform magnetic field.     

Theory of self-focusing in a hollow waveguide

We present a theoretical investigation of self-focusing in a hollow waveguide filled with noble gas. Our analysis was performed for a laser pulse that was predominantly in the fundamental mode and revealed the physical processes involved in self-focusing in a hollow waveguide. A critical power for self-focusing was obtained that was found to be substantially higher than the critical power for self-focusing in a bulk medium. Useful design criteria for pulse-compression systems are presented. We identify the parameter range for which the transverse variation of the pulse phase introduced by the Kerr nonlinearity is small.     

A path integral approach to inclusive processes

The single-particle inclusive differential cross-section for a reaction is written as the imaginary part of a correlation function in a forward scattering amplitude for in a modified effective theory. In this modified theory the interaction Hamiltonian equals in the original theory up to a certain time. Then there is a sign change and becomes nonlocal. This is worked out in detail for scalar field models and for QED plus the abelian gluon model. A suitable path integral for direct calculations of inclusive cross sections is presented. Received: 8 March 2000 / Published online: 6 July 2000     

The experimental investigation of a glow discharge in a toroidal tube

A glow discharge in a toroidal tube with axial discharge current is investigated. The investigation was carried out for a discharge as a whole, not for electrodal zones and the positive column separately. The volt-ampere characteristics for different pressures and Paschen's curves for different gases were measured. The curves obtained are compared with analogous ones for a cylindrical tube. The conditions for the existence of a glow discharge in a toroidal tube and the processes passing there are discussed on the basis of the measured curves. The experiments were carried out in air, helium, argon and neon.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

Detection and discrimination of spectral peaks and notches at 1 and 8 kHz

The ability of subjects to detect and discriminate spectral peaks and notches in noise stimuli was determined for center frequencies fc of 1 and 8 kHz. The signals were delivered using an insert earphone designed to produce a flat frequency response at the eardrum for frequencies up to 14 kHz. In experiment I, subjects were required to distinguish a broadband reference noise with a flat spectrum from a noise with either a peak or a notch at fc. The threshold peak height or notch depth was determined as a function of bandwidth of the peak or notch (0.125, 0.25, or 0.5 times fc). Thresholds increased with decreasing bandwidth, particularly for the notches. In experiment II, subjects were required to detect an increase in the height of a spectral peak or a decrease in the depth of a notch as a function of bandwidth. Performance was worse for notches than for peaks, particularly at narrow bandwidths. For both experiments I and II, randomizing (roving) the overall level of the stimuli had little effect at 1 kHz, but tended to impair performance at 8 kHz, particularly for notches. Experiments III-VI measured thresholds for detecting changes in center frequency of sinusoids, bands of noise, and spectral peaks or notches in a broadband background. Thresholds were lowest for the sinusoids and highest for the peaks and notches. The width of the bands, peaks, or notches had only a small effect on thresholds. For the notches at 8 kHz, thresholds for detecting glides in center frequency were lower than thresholds for detecting a difference in center frequency between two steady sounds. Randomizing the overall level of the stimuli made frequency discrimination of the sinusoids worse, but had little or no effect for the noise stimuli. In all six experiments, performance was generally worse at 8 kHz than at 1 kHz. The results are discussed in terms of their implications for the detectability of spectral cues introduced by the pinnae.     

A new method for calculating the Zeeman split acceptor levels in cubic semiconductors

Within the effective-mass approximation we introduce a transformed hamiltonian for the acceptor problem in a homogeneous magnetic field. The new hamiltonian is expressed entirely in terms of spherical tensor operators. The reduced-matrixelement technique can thus be used in solving variationally the eigenvalue problem. In this way a simple non-perturbation numerical calculation of the Zeeman split acceptor states becomes for the first time feasible. As a preparatory test for the method we used the new hamiltonian in a variational “model” calculation with a very restricted basis set, to calculate the linear Zeeman parameters for some excited states of shallow acceptors in Ge and GaAs. The results can be compared with recent experimental data for these materials. We find already an excellent numerical agreement between the calculated and the measured linear Zeeman parameters for the final states of the D-transitions, and we obtain the correct order of magnitude for those of the C-line final states.     

“Vacuum” friction and heat exchange of a nano- and a microparticle with a solid surface

The most general relativistic formulas for the tangential force of the fluctuation-electromagnetic interaction and the rate of thermal heating of a spherical neutral particle moving in vacuum near the surface of a condensed medium are obtained for the first time in dipole approximation. It is shown that the existence of a fluctuation-induced magnetic moment for a conducting particle is responsible for a considerable increase in the vacuum heat-exchange rate as compared to contact and radiative heat transfer (in accordance with the Stefan law). It is noted that the coincidence of the absorption peaks for the particle and the surface in the microwave range can explain the damping forces observed for nanoprobes in the dynamic mode of the atomic force microscope.     

Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.     

Detecting the inseparability and distillability of continuous variable states in Fock space

The partial transposition (PT) operation is an efficient tool in detecting the inseparability of a mixed state. We give an explicit formula for the PT operation for the continuous variable states in Fock space. We then give the necessary and sufficient condition for the positivity of Gaussian operators. Based on this, a number of criteria on the inseparability and distillability for the multimode Gaussian states are naturally drawn. We finally give an explicit formula for the state in a subspace of a global Gaussian state. This formula, together with the known results for Gaussian states, gives the criteria for the inseparability and distillability in a subspace of the global Gaussian state.     

Compact multireference wavefront sensor design

We present a compact optical design for a multireference Shack-Hartmann-based wavefront sensor (WFS) for multiconjugate adaptive optical systems. The key component of this WFS design is a field lenslet array that separates the exit pupil images in the sensing plane for all reference sources. An analytical method for WFS optical design is presented, and the optimal strategy for selecting optical components from a discrete set is outlined. The feasibility of the WFS design has been demonstrated for a prototype WFS system in a laboratory setup with five reference sources and two deformable mirrors representing a wavefront-distorting medium.     

Information capacity of optical fiber channels with zero average dispersion

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying analytical expressions for the output probability density functions both for a nonlinear channel and for a linear channel with additive and multiplicative noise we calculate in a closed form a lower bound estimate on the Shannon capacity for an arbitrary signal-to-noise ratio.     

Critical power for self-focusing in bulk media and in hollow waveguides

We determine the threshold power for self-focusing collapse both in a bulk medium and in a hollow-core waveguide for various spatial profiles. We find that the threshold power for collapse in the waveguide is always equal to the lower-bound prediction for a bulk medium.     

Dynamics of texture for spinor condensates

We study a dynamics of texture for a two-component spinor bose condensate. This is carried out by adopting a time dependent Landau-Ginzburg Lagrangian for a spinor order parameter. By using a polar form of the spinor order parameter, we obtain a field equation for the texture. In particular we consider a one dimensional model in which we can obtain analytic forms for the textures in terms of elliptic functions of several kinds. We find that these solutions are characterized by a modulus parameter, and changes in this parameter cause structural changes of texture.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

Transport in a fluctuating potential

We study the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. The potential has no inversion symmetry, and the fluctuations are correlated in time. At finite temperatures, a stationary current is induced. The amplitude and the direction of the current depend on the details of the noise process that is responsible for the potential fluctuations. We discuss several limiting situations for a general case. Furthermore we calculate the current in the case of a piecewise linear potential for different noise processes and parameters. A detailed discussion of the results is given, including a discussion of the mechanism that is responsible for the current reversal. We compare the present results with results for transport in a ratchet-like potential due to a fluctuating force. We also discuss the biological relevance of the present models for molecular motors. We present a model for the motion of molecular motors that explains why similar molecular motors can move in different directions.     

Intensity cross-correlation in light scattered by the rotational motion of macromolecules

Intensity cross-correlation in light scattered by the rotational motion of macromolecules is discussed in terms of pair- pair correlation. Expressions are given for a single pair for comparison with a rod, an equilateral triangle for comparison with a flat macromolecule, and a regular tetrahedron for comparison with other shapes. Anticorrelation occurs for the pair and triangle and correlation for the tetrahedron.