Related papers: Path integral derivations of novel complex traject…
Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. In addition, they provide a natural way to describe optical excitation with complex fields…
L\'{e}vy flights can be described using a Fokker-Planck equation which involves a fractional derivative operator in the position co-ordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show…
Using the path integral measure factorization method based on the nonlinear filtering equation from the stochastic process theory, we consider the reduction procedure in Wiener path integrals for a mechanical system with symmetry that…
A new approach to the description of inhomogeneous disk-loaded waveguides (chains of coupled resonators) is proposed. New matrix difference equations based on the technique of coupled integral equations and the decomposition method are…
We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
A comparative study of different block matching alternatives for motion estimation is presented. The study is focused on computational burden and objective measures on the accuracy of prediction. Together with existing algorithms several…
The results of the development of an approximate approach, which can be considered as an analogue of the WKB method, are presented. This approach gives possibility to divide the electromagnetic field in structured waveguides into forward…
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…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…
We build a setup for path integral quantization through the Faddeev-Jackiw approach, extending it to include Grassmannian degrees of freedom, to be later implemented in a model of generalized electrodynamics that involves fourth-order…
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…
The indeterminate nature of human motion requires trajectory prediction systems to use a probabilistic model to formulate the multi-modality phenomenon and infer a finite set of future trajectories. However, the inference processes of most…
The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir-Polder energies. An important challenge arises when one desires derivatives of path-integral quantities--standard finite-difference…