Related papers: Path Integral Analysis of Arrival Times with a Com…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
We propose a distributed algorithm to solve a dynamic programming problem with multiple agents, where each agent has only partial knowledge of the state transition probabilities and costs. We provide consensus proofs for the presented…
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than…
The high computational expense of simulating light through ray-tracing in large, sparsely instrumented particle detectors such as IceCube and Antares is a critical outstanding problem in particle physics. When the detector is sparsely…
We formulate quantum tunneling as a time-of-arrival problem: we determine the detection probability for particles passing through a barrier at a detector located a distance L from the tunneling region. For this purpose, we use a…
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…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
We propose an idea of the constrained Feynman amplitude for the scattering of the charged lepton and the virtual W-boson, $l_{\beta} + W_{\rho} \rightarrow l_{\alpha} + W_{\lambda}$, from which the conventional Pontecorvo oscillation…
We calculate the admittance of a two-dimensional quantum point contact (QPC) using a Boltzman-like kinetic equation derived for a partial Wigner distribution function in an effective potential. We show that this approach leads to the known…
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion,…
We investigate the use of stochastic methods for zero energy quantum scattering based on a path integral approach. With the application to the scattering of a projectile from a nuclear many body target in mind, we use the potential…
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…
A traffic incident analysis method based on extended spectral envelope (ESE) method is presented to detect the key incident time. Sensitivity analysis of parameters (the length of time window, the length of sliding window and the study…