We investigate the scattering of a charged quantum particle in a helically twisted background that induces an effective Coulomb-like interaction, in the presence of an Aharonov-Bohm (AB) flux. Starting from the nonrelativistic Schrödinger equation in the twisted metric, we derive the radial equation and show that, after including the AB potential, it can be mapped onto the same Kummer-type differential equation that governs the planar
2D Coulomb
+ AB problem, with a geometry-induced Coulomb strength and the azimuthal quantum number shifted as
m→m−λ. We construct the exact scattering solutions, obtain closed expressions for the partial-wave
S matrix and phase shifts, and derive the corresponding scattering amplitude, differential cross section, and total cross section. We also show that the pole structure of the
S matrix is consistent with the bound-state quantization previously obtained for the helically twisted Coulomb-like problem.
In this paper we formulate the hydrodynamic moment and cumulant expansions of the density matrix for a quantum system in which the time evolution is described by an infinite hierarchy of coupled hydrodynamic moment equations. For the case where the system interacts with a complex environment, we develop a semiclassical closure that truncates the hierarchy. Our numerical approach for solving the truncated system of equations is intimately related to the de Broglie−Bohm interpretation of quantum mechanics, in that the time evolution of each cumulant is constructed over a discrete ensemble of hydrodynamic paths. We discuss the advantages and disadvantages of this scheme and apply the method to a model problem for a particle escaping from a metastable potential well while in contact with a thermal bath.