Particle-hole symmetry and the nu=5/2 quantum Hall state

We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.     

Aharonov-Bohm shift as a shift in normal coordinates

The Aharonov-Bohm shift in a closed system is considered. The solenoid is a charged, rotating cylinder which is electrically neutral. This model of Henneberger and Opatrny has a Hamiltonian which is a quadratic form. This quadratic form is transformed to normal coordinates, so that the stationary states become self-evident. It is shown that, in the original system, it is the kinetic angular momentum which is quantized. Solutions of the problem for an electron inside the solenoid are discussed. It is shown that the rotating cylinder exhibits different behavior if the electron is in the magnetic field or if it is in the external region. An external field approximation which replaces the cylinder by a constant magnetic field therefore cannot yield a correct solution of the Schrödinger equation which is continuous at the surface of the solenoid.     

Recording of time-varying electrical signals with one-dimensional holograms

A method of optically recording and reconstructing electrical signals in the form of one-dimensional holograms is described. For this purpose a pulsed laser beam is modulated according to the information to be stored. This beam is superimposed on a spatially and temporally constant reference beam, and the resulting interference pattern is recorded on a film which is moved past the light distribution. The one-dimensional holograms thus recorded appear arranged in narrow tracks which partially overlap.For reconstruction the film is driven past a spatially and temporally constant reconstructing wave. The illuminated holograms reconstruct a closely spaced chain of points which successively pass by a detector in which they produce an alternating current which, after appropriate amplification and filtering, presents the original signal.     

Soluble model of a single component fermion interacting with a vector meson

A model is formulated in two dimensional spacetime in which a massive vector meson is coupled to only the upper or the lower component of the usual two component fermion field operator. This condition implies a unique (nonconserved) V ± A form for the current, a result which is equivalent to the statement that the current is either self-dual or anti-self-dual. The Green's functions of the model are computed using the device of the external source. A significant result which emerges is the fact that the renormalized meson mass is not a polynomial form in the coupling constant, a situation which has not previously occurred in any of the known soluble field theories. Although there is no limit of this model in which one can obtain the Thirring model, it is shown that a particular solution of the latter can be obtained provided that one considers only configurations in which all fermion excitations are moving to the left or all are moving to the right.     

Deconfinement and phase diagram of bosons in a linear optical lattice with a particle reservoir

We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose-condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state.     

Energy basis via decoherence

The question of the emergence of a preferred basis which is generally understood as that basis in which the reduced density matrix is driven to a diagonal (classically interpretable) form via environment induced decoherence is addressed. The exact solutions of the Caldeira-Leggett Master Equation are analyzed for a free particle and a harmonic oscillator system. In both cases, we see that the reduced density matrix is driven diagonal in the energy basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the preferred basis which is contrary to the general notion that it is the position basis which is selected since the coupling to the environment is via the position coordinates     

Price dynamics from a simple multiplicative random process model

The existence of stylized facts suggests that there might be `universal' mechanism which drives price evolution on financial markets in general. Based on empirical estimates of 10 major indices, we propose a stylized model of endogenous price formation on an aggregate level whose key issue is that price evolution is driven by the `market's' expectations about future growth rates of investment. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics which admits some far reaching formal analysis. Generated return trails exhibit statistical properties such as 'volatility clustering', multi scaling, and a non-Gaussian distribution which is in quantitative in agreement with stylized facts from empirical asset returns. Additionally non-equilibrium entropies are also considered. These results suggests that the structure of the model mimicks a mechanism which is essential in driving price dynamics of financial markets in general.     

Hybrid quintessential inflation

A model is presented in which a single scalar field is responsible for both primordial inflation at early times and then dark energy at late times. This field is coupled to a second scalar field which becomes unstable and starts to oscillate after primordial inflation, thus driving a reheating phase that can create a high post-inflation temperature. This model easily avoids overproduction of gravity waves, which is a problem in the original quintessential inflation model in which reheating occurs via gravitational particle production.     

A General Theory of Non-Abelian Electrodynamics

The general theory of gauge fields is used to develop a theory of electrodynamics in which the fundamental structure is non-Abelian and in which the internal gauge field symmetry is O(3), based on the existence of circular polarization and the third Stokes parameter. The theory is used to provide an explanation for the Sagnac effect with platform at rest and in motion. The Sagnac formula is obtained by considering the platform in motion to be a gauge transformation. The topological phases can be described straightforwardly with non Abelian electrodynamics, which produces a novel magnetic field component for all types of radiation, a component which is proportional to the third Stokes parameter. The theory provides a natural explanation for the inverse Faraday effect without phenomenology.     

Self-oscillations in a hybrid bistable optical device

The Van der Pol, Krylov-Bogoliubov method for self-oscillation calculations in nonlinear systems is applied to a piezoelectrically driven Fabry-Perot interferometer which is operated as a hybrid bistable optical device. It is shown that in cases where the time delay in the feedback signal cannot be ignored, or when a reactive element is inserted in the appropriate place in the electrical circuit, self-oscillation will result. Experiments in which a piezoelectric element serves as the basic component of a hybrid bistable device demonstrate that self-oscillation occurs with a frequency which is very near the piezoelement self-frequency.     

Finite element model for waves guided along solid systems of arbitrary section coupled to infinite solid media

The Semi-Analytical Finite Element (SAFE) method is becoming established as a convenient method to calculate the properties of waves which may propagate in a waveguide which has arbitrary cross-sectional shape but which is invariant in the propagation direction. A number of researchers have reported work relating to lossless elastic waves, and recently the solutions for nonpropagating waves in elastic guides and for complex waves in viscoelastic guides have been presented. This paper presents a further development, addressing the problem of attenuating waves in which the attenuation is caused by leakage from the waveguide into a surrounding material. This has broad relevance to many practical problems in which a waveguide is immersed in a fluid or embedded in a solid. The paper presents the principles of a procedure and then validates and illustrates its use on some examples. The procedure makes use of absorbing regions of material at the exterior bounds of the discretized domain.     

Long-range intensity correlation and the approach to localization

The influence of internal surface reflectivity is incorporated into a heuristic model of long-range intensity correlation. This allows us to identify the spatial intensity correlation function in a sample of randomly positioned polystyrene spheres as the sum of a first-order term in the correlation parameter κ, which falls linearly with detector separation, and a constant term, which is of order κ². κ is a measure of the proximity to the localization threshold. In a sample which is a mixture of metallic and dielectric spheres and in which κ becomes large, the probability of large intensity fluctuations increases. The distribution of intensities is then found to be stretched exponential even for sample lengths which are comparable to the wavelength of the radiation.     

Long-range intensity correlation and the approach to localization

Abstract

The influence of internal surface reflectivity is incorporated into a heuristic model of long-range intensity correlation. This allows us to identify the spatial intensity correlation function in a sample of randomly positioned polystyrene spheres as the sum of a first-order term in the correlation parameter κ, which falls linearly with detector separation, and a constant term, which is of order κ². κ is a measure of the proximity to the localization threshold. In a sample which is a mixture of metallic and dielectric spheres and in which κ becomes large, the probability of large intensity fluctuations increases. The distribution of intensities is then found to be stretched exponential even for sample lengths which are comparable to the wavelength of the radiation.     

Evaluation of the decay in temporal coherence of a laser beam propagating in a slowly fluctuating medium

A simple method is described for evaluating the change in temporal coherence which occurs when a monochromatic light wave traverses a medium the properties of which fluctuate randomly. The degree of second-order coherence is formulated in terms of the amplitude and phase autocorrelation functions which are derived from the photocurrent produced in a light beating experiment. This method makes it possible to evaluate even a small deterioration in temporal coherence which is closely related to the frequency fluctuations in the light wave. The change in temporal coherence of a laser beam propagating through a slowly fluctuating gaseous path has been measured.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

Typicality vs. Probability in Trajectory-Based Formulations of Quantum Mechanics

Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown that the explanation does not make use of the full probability measure, but rather of a suitable set function deriving from it, which defines relative typicality between single-time cylinder sets. Such a set function can also be derived directly from the standard quantum formalism, without the need of an underlying probability measure. The key concept for this derivation is the quantum typicality rule, which can be considered as a generalization of the Born rule. The result is a new formulation of quantum mechanics, in which particles follow definite trajectories, but which is based only on the standard formalism of quantum mechanics.     

Derivation of Some Translation-Invariant Lindblad Equations for a Quantum Brownian Particle

We study the dynamics of a Brownian quantum particle hopping on an infinite lattice with a spin degree of freedom. This particle is coupled to free boson gases via a translation-invariant Hamiltonian which is linear in the creation and annihilation operators of the bosons. We derive the time evolution of the reduced density matrix of the particle in the van Hove limit in which we also rescale the hopping rate. This corresponds to a situation in which both the system-bath interactions and the hopping between neighboring sites are small and they are effective on the same time scale. The reduced evolution is given by a translation-invariant Lindblad master equation which is derived explicitly.     

Semiconductor Optical Amplifier (SOA)-Fiber Ring Laser for Sensor Application

A bi-directional fiber ring laser with a semiconductor optical amplifier has been developed in which a frequency difference between the counter-propagating oscillations is controlled by an introduced birefringent medium. With the material which causes the retardation change by a physical phenomenon to be measured, the laser in this study is applicable to a novel fiber sensor of which the sensing signal is obtained in a frequency domain.     

Quantum Phenomena in a Classical Model

This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.     

用电流源法测量非线性元件的伏安特性

本文报导了一种新的用于测量非线性元件伏安特性的实验电路，该电路采用的是以电流为信号变量的电流模式测量电路，并分析与比较了该电路与传统的以电压作为信号变量的电压模式测量电路的不同．