相关论文: Fractional WKB Approximation

Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…

This paper presents the derivation of Schwinger's gauge invariant result of $Im \cal{L}_{eff}$ upto one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation…

We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr\"odinger propagator when the potential is quadratic at infinity. This construction is based on the…

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…

Gutzwiller projection allows a construction of an assortment of variational wave functions for strongly correlated systems. For quantum spin S=1/2 models, Gutzwiller-projected wave functions have resonating-valence-bond structure and may…

We construct a wavelet-based almost sure uniform approximation of fractional Brownian motion (fBm) B_t^(H), t in [0, 1], of Hurst index H in (0, 1). Our results show that by Haar wavelets which merely have one vanishing moment, an almost…

We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic incident wave. We introduce a potential for which the far field…

In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…

The paper presents the results of a study of the possibility of using the WKB approach to describe Inhomogeneous Travelling-Wave Accelerating Sections (ITWAS). This possibility not only simplifies the calculation, but also allows the use of…

We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving…

In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated…

We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…

By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…

Gutzwiller wavefunction is a physically well motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate evaluation of the expectation value of any operator within…

The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

In this work we present the results of calculation of the electric field distribution in the inhomogeneous media based on the generalized WKB method. In this approach the field is represented as the sum of two components, one of which is…

The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…

Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…