Path Integral Formulation for Chern-Simons Quantum Mechanics

Chern-Simons quantum mechanics is studied by using the path integral formulation. We find that the model can be decomposed into two independent oscillators when a set of new coordinate is chosen. The propagator is constructed in this new set of coordinate and the spectra is read off directly from it. The spectra will be divergent when the mass of the particle tends to zero. In order to get a physical result, one must regularize the spectra properly. We afford a new scheme of regularization. Interestingly, our scheme shows that the regularization we proposed amounts to erase one of the oscillators in the new set of coordinate. Physical interpretations for the regularization are given and some ambiguities in the literatures are clarified.     

Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

We elaborate and compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for a purely dissipative isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.     

A Path Integral Approach¶to the Kontsevich Quantization Formula

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra. Received: 10 March 1999 / Accepted: 30 January 2000     

Hooke＇s Atom in an Arbitrary External Electric Field： Analytical Solutions of Two-Electron Problem by Path Integral Approach

By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analyticalsolutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.     

Calculation of Internal Energy and Pressure of Dense hydrogen Plasma by Direct Path Integral Monte Carlo Approach

The internal energy and pressure of dense hydrogen plasma are calculated by the direct path integral Monte Carlo approach. The Kelbg potential is used as interaction potentials both between electrons and between protons and electrons in the calculation. The complete formulae for internal energy and pressure in dense hydrogen plasma derived [or the simulation are presented. The correctness of the derived formulae are validated by the obtained simulation results. The numerical results are discussed in details.     

Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field

The conformally gauge-fixed Polyakov D1 brane action in the presence of a scalar dilaton field is seen to be a constrained system in the sense of Dirac. In the present work we study its Hamiltonian and path integral quantization in the instant-form of dynamics using the equal world-sheet time framework.     

Zero-Point Vacancy Concentration in a Model Quantum Solid: A Reversible-Work Approach

We investigate the influence of anharmonic effects on the zero-point vacancy concentration in a boson system model in the solid phase at T=0 K. We apply the reversible-work method to compute the vacancy formation free energy and the vacancy concentration in the system. A comparison of our results with those obtained using the harmonic approximation show that anharmonic effects reduce the formation free energy by ∼25%, leading to an increase of the zero-point vacancy concentration by more than an order of magnitude.     

Brownian Motion of a Charged Particle in Electromagnetic Fluctuations at Finite Temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.     

Non-equilibrium Wall Deposition of Inertial Particles in Turbulent Flow

Non-equilibrium effects resulting from the slow relaxation of inertial particles to statistical equilibrium with flow fluctuations in turbulence are known to have important consequences, but they are not readily incorporated into models. Here, a simple analysis of these effects predicts −2/3 power-law dependence of the particle deposition rate on Stokes number (normalized particle inertia) in the far field of a confined turbulent flow, and a weaker near-field dependence. Near-field measurements and numerical simulations exhibit this weaker dependence, as do models that are generally viewed as validated by this result, but the models fail to capture the newly identified far-field behavior due to their equilibrium assumptions. Quantification of these qualitative observations is obtained by incorporating particle response to fluid motion into ‘one-dimensional turbulence’ (ODT), a stochastic computational model of turbulence.     

Finite-Time Fluctuations in the Degree Statistics of Growing Networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.     

Fluctuations in a lévy flight gas

We consider the density fluctuations of an ideal Brownian gas of particles performing Lévy flìghts characterized by the indexf. We find that the fluctuations scale as N(t) t^H, where the Hurst exponentH locks onto the universal value 1/4 for Lévy flights with a finite root-mean-square range (f>2). For Lévy flights with a finite mean range but infinite root-mean-square range (1相似文献   

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

Effects of a rectangular aperture on the vectorial structure of a Gaussian beam in the far-field regime

With the help of the angular spectrum representation and the Gaussian function expansions of the hard-edge aperture function, the vectorial structure of a linearly polarized Gaussian beam (GB) diffracted by a rectangular aperture is analyzed in detail. It is found that the sizes of the energy flux density spots and the energy fluxes of the TE and TM terms depend on the aperture configuration and the polarization direction of the incident GB. The far fields may have smaller spots and larger energy fluxes for a GB diffracted by a rectangular aperture compared to that by a square aperture with the same beam intensity. And another potential application in information encoding and transmission for free-space communications is also proposed in addition to re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

Solitons in Plasmas: A Lie Symmetry Approach

This paper talks about the stationary solitons for Langmuir waves in plasmas that are described by the Nonlinear Schrödinger’s equation with power law nonlinearity. The integration is carried out by the usage of Lie symmetry in presence of perturbation terms.     

Improved gate-control in InAs nanowire structures by the use of GdScO3 as a gate dielectric

We investigated the properties of gadolinium scandate (GdScO₃) as a gate dielectric for top-gate electrodes on undoped InAs nanowires. It is demonstrated that due to the high dielectric constant of GdScO₃ (k=22), a better control of the conductance of the nanowire is achieved compared to a reference SiO₂-isolated back-gate electrode. We analyzed the output and transfer characteristics of top-gate-controlled InAs wires at room temperature and at temperatures down to 4 K. Owing to the good coverage of the InAs nanowire by the 50-nm-thick GdScO₃ layer, which was deposited by pulsed-laser deposition, the gate leakage current is sufficiently suppressed.     

Generation of picoseconds stimulated Raman scattering in a BaWO4 crystal and frequency up-conversion by difference-frequency generation in BBO

The characters of stimulated Raman scattering of BaWO₄ crystal excited by a picoseconds laser at 1064 nm are studied based on optical parametric amplification (OPA). Up to six-order Stokes components and five-order anti-Stokes components are observed. The SRS components are amplified by an OPA and the wavelength tunable range from 411 to 2594 nm is achieved with a maximum conversion efficiency of 38% using the OPA stage.     

Laser-based sensor for a coolant leak detection in a nuclear reactor

Currently, the nuclear industry needs strongly a reliable detection system to continuously monitor a coolant leak during a normal operation of reactors for the ensurance of nuclear safety. In this work, we propose a new device for the coolant leak detection based on tunable diode laser spectroscopy (TDLS) by using a compact diode laser. For the feasibility experiment, we established an experimental setup consisted of a near-IR diode laser with a wavelength of about 1392 nm, a home-made multi-pass cell and a sample injection system. The feasibility test was performed for the detection of the heavy water (D₂O) leaks which can happen in a pressurized heavy water reactor (PWHR). As a result, the device based on the TDLS is shown to be operated successfully in detecting a HDO molecule, which is generated from the leaked heavy water by an isotope exchange reaction between D₂O and H₂O. Additionally, it is suggested that the performance of the new device, such as sensitivity and stability, can be improved by adapting a cavity enhanced absorption spectroscopy and a compact DFB diode laser. We presume that this laser-based leak detector has several advantages over the conventional techniques currently employed in the nuclear power plant, such as radiation monitoring, humidity monitoring and FT-IR spectroscopy.     

Functional Integral Approach to the Transition Temperature of Attractive Interacting Bose Gas in Traps

The functional integral approach (FIA) is introduced to study the transition temperature of an imperfect Bose gas in traps. An interacting model in quantum statistical mechanics is presented. With the model we study a Bose gas with attractive interaction trapped in an external potential, We obtain the result that the transition temperature of a trapped Bose gas will slightly shift upwards owing to the attractive interacting force. Successful application of the FIA to Bose systems is demonstrated.