Feynman integral treatment of the Bargmann potential

A method based on path integral formulation is given for obtaining exact solution of the s states for the Bargmann potential

     

Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation

The expressions of the refractive indices corresponding wave vector k(θ,) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by

and that of the wave, whose velocity is faster, is given by

     

Singular ring solutions of critical and supercritical nonlinear Schrödinger equations

We present new singular solutions of the nonlinear Schrödinger equation (NLS)

     

Spin in the worldline path integral in 2 + 1 dimensions

We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x(τ), the spacetime paths. We then show that the functional integral automatically imposes the constraint , while there is a spin action, which agrees with the one one should expect for a spin- field.     

Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles

The N-dimensional Hamiltonian

     

A general formula of two-dimensional Franck-Condon integral and the photoelectron spectroscopy of sulfur dioxide

We derived a general formula of Franck-Condon integral for two-dimensional harmonic oscillators () taking into account the Duschinsky effect and applied it to study the photoelectron spectroscopy of SO₂ and . The equilibrium geometries and harmonic vibrational frequencies of , SO₂ and were calculated by using the density functional theory (B3LYP functional) and the coupled cluster singles and doubles with perturbative triples [CCSD(T)] methods with various basis sets up to 6-311+G(3df) and aug-cc-pVTZ. The adiabatic ionization energy and electron affinity were computed by using the CCSD(T) method extrapolated to the complete basis set limit with aug-cc-pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both SO₂ and are in accord with the experiment. While the Duschinsky effect plays a role for some weak transitions of SO₂, it can be neglected for . A splitting observed in the experimental photoelectron spectrum of SO₂ is interpreted as contributing from hot bands and combination bands of ν₁ and ν₂, rather than arising from perturbation of a potential barrier as previous researchers proposed. The calculated adiabatic ionization energy and electron affinity are in agreement with the experiment within 0.027 and 0.040 eV, respectively.     

Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution:

     

Blow-up of solution of an initial boundary value problem for a generalized Camassa-Holm equation

In this Letter, we study the following initial boundary value problem for a generalized Camassa-Holm equation

     

Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays

In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov-Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay h(t) satisfies and the decay rate β can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., and β satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.     

Radiation transfer in an inhomogeneous half-space

The emergent flux for radiation transfer in an inhomogeneous half-space for a new choice of c(x)

     

Thermoalgebras and path integral

Using a representation for Lie groups closely associated with thermal problems, we derive the algebraic rules of the real-time formalism for thermal quantum field theories, the so-called thermo-field dynamics (TFD), including the tilde conjugation rules for interacting fields. These thermo-group representations provide a unified view of different approaches for finite-temperature quantum fields in terms of a symmetry group. On these grounds, a path integral formalism is constructed, using Bogoliubov transformations, for bosons, fermions and non-abelian gauge fields. The generalization of the results for quantum fields in topology is addressed.     

Kinetic modelling of gibbsite dehydration/amorphization in the temperature range 823-923 K

In this work, the kinetics of gibbsite dehydration/amorphization were investigated in the temperature range from 823 to 923 K. Different kinetic models were evaluated to find the appropriate formalizations that best describe or predict the kinetic behavior of this process. Gibbsite dehydration/amorphization is a complex process involving a set of chain reactions:

     

Coupling efficiency of laser beam to multimode fiber

The coupling efficiency of laser beam to multimode fiber is given by geometrical optics, and the relation between the maximum coupling efficiency and the beam propagation factor M² is analyzed. An equivalent factor for the multimode fiber is introduced to characterize the fiber coupling capability. The coupling efficiency of laser beam to multimode fiber is calculated in respect of the ratio by the overlapping integral theory. The optimal coupling efficiency can be roughly estimated by the ratio of M² to but with a large error range. The deviation comes from the lacks of information on the detail of phase and intensity profile in the beam factor M².