Related papers: On the numerical evaluation of real-time path inte…
The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…
In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In these decades, some useful formulas for the Fourier transform…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
Sharp-momentum transition matrix elements for scattering from a short-range Gaussian potential are computed using a real-time path integral. The computation is based on a numerical implementation of a new interpretation of the path integral…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes…
We discuss the method to compute the integrals which appear in the retarded potential term for a real-time simulation based on QED (Quantum Electrodynamics). We show that the oscillatory integrals over the infinite interval involved in them…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
In this paper, we propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar L\'evy processes. The method is based on the accurate numerical formulas for Fourier…
We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…