Related papers: Reconciling Semiclassical and Bohmian Mechanics: I…
Complex, non-Hermitian potentials V(x) can often generate standard quantum bound states. H. F. Jones [Phys. Rev. D 78, 065032 (2008)] demonstrated that the idea cannot directly be transferred to scattering. We reveal that a return to the…
A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…
We assume that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter $1/\sqrt{\Omega}$. The system stationary state…
The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics.…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They…
The full set of stationary states of the mean field of a Bose-Einstein condensate in the presence of a potential step or point-like impurity are presented in closed analytic form. The nonlinear Schr\"odinger equation in one dimension is…
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
A nonlinear quantum-classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schr\"{o}dinger equation is proved. The dissipative dynamics is…
It is shown that non-stationary solutions of the Schr\"{o}dinger equation, which describes the quantum dynamics of a particle in the field of a one-dimensional delta potential (1DDP), are divided into two classes: some define pure states…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
Systems with space-periodic Hamiltonians have unique scattering properties. The discrete translational symmetry associated with periodicity of the Hamiltonian creates scattering channels that govern the scattering process. We consider a…
We take up the idea of Nelson's stochastic processes, the aim of which was to deduce Schr\"odinger's equation. We make two major changes here. The first one is to consider deterministic processes which are pseudo-random but which have the…
With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…