Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Behavior of a quantum particle in contact with a classical heat bath

We investigate the behavior of a two-level quantum system in contact with a classical heat bath, e.g., a solute particle with internal degrees of freedom immersed in a solvent of massive particles. Using a combination of analytical and numerical methods, we obtain precise information about localization, time-displaced correlation functions, and the frequency-dependent susceptibility of such solute particles. We find that these quantities can have a strong dependence on the density of the solvent fluid, with the maximum changes from the behavior of the corresponding isolated quantum system occurring in many cases at very low densities. We compare the exact results with those obtained by path integral Monte Carlo. There is good agreement with the imaginary time correlations, but analytic continuation to real time proves elusive: even with the best numerical data on the former, we can only get very gross features of the latter.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

Revisiting Gouy phase

The aim of this paper is to highlight the added value of the generalized Gouy phase shift introduced by Siegman. Although suited for optical systems study, including those more complex than free space, we note that it did not meet the use that it deserves so far. The analysis of the whole of the ideas and analytical approaches associated to the important concept of the Gouy phase proves its effectiveness.

Usually, the resonance condition is systematically built on the basis of the equivalent empty cavity. Unfortunately, this approach does not cover some of the useful parameters of the real resonator. By means of the generalized Gouy phase and the self-consistent complex parameter q, we derive here a new approach for the calculation of the resonance condition for the real cavity. Moreover, the use of the generalized Gouy phase clearly simplifies the study of resonators, while making it possible to avoid the use of the Huygens’ Fresnel integral.     

The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas

Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is botained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Resibois‘ method,we present the first principle formula of the relativistic heat conductivity of Coulumb electronic plasmas for low-order corrections.     

EFFECTS OF CONSTRAINTS ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF A BIRKHOFF SYSTEM

After a Birkhoff system is restricted by constraints, the determining equations, the Lie symmetries, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some Lie symmetries will disappear and under certain conditions some Lie symmetries will still remain present. The condition under which Lie symmetries and conserved quantities of the system will remain is given.     

Half-Width Integral Method for Gas Concentration Measuring in Tunable Diode Laser Absorption Spectroscopy

ABSTRACT

We analyze the influence of random errors and absorption shape fitting errors on gas concentration measurement in tunable diode laser absorption spectroscopy. We then propose a new data processing method according to the characteristic of random errors and fitting absorption shape. This method only uses the integral value within the half width at half maximum of the fitting absorption shape to determine the gas concentration in actual measurements. Meanwhile, the O₂ transition at 13,150.197 cm^?1 is selected to measure the O₂ concentration using this method. Compared with the traditional method, the method established in this paper can accurately measure O₂ concentration.