Related papers: The Maslov correction in the semiclassical Feynman…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…
I study the quantum mechanics of a spin interacting with an ``apparatus''. Although the evolution of the whole system is unitary, the spin evolution is not. The system is chosen so that the spin exhibits loss of quantum coherence, or…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the…
The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of…
The contribution of different modes of the Coulomb field to decoherence and to the dynamical breakdown of the time reversal invariance is calculated in the one-loop approximation for non-relativistic electron gas. The dominant contribution…
In this work we show an error estimate for a first order Gaussian beam at a fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For the caustic that we study the exact solution can be constructed using Airy…
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…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
We write a space-time Feynman path integral representation for scattered elastic wave fields from a weakly compact supported anisotropic non-homogeneity.Replacement by a new version where We (I!) propose a new tomographic inversion…
Oscillating integrals often arise in the theoretical description of phenomena in chemical physics, in particular in atomic and molecular collisions, and in spectroscopy. A computer code for the numerical evaluation of the oscillatory…
Using thermodynamic arguments treatment it is shown that, independently on whether Fisher renormalization changes the critical exponents near a phase transition in a constrained system or not, new corrections to scaling with correction…