Related papers: Optical Aharonov-Bohm effect: an inverse hyperboli…
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
Signs of hypothetical light gauge bosons from a hidden sector may appear in Aharonov-Bohm-like experiments. The absence of signal in carried on experiments allow us to set a modest constraint to the mass and coupling constant of these…
Using the theory of self-adjoint extensions, we construct all the possible hamiltonians describing the non relativistic Aharonov-Bohm effect. In general the resulting hamiltonians are not rotationally invariant so that the angular momentum…
We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. Our solution produces a renormalization group (RG) transformation to all orders in…
Inverted-band $pn$ junctions in two-dimensional materials offer a promising platform for electron optics in condensed matter, as they allow to manipulate and guide electron beams without the need for spatial confinement. In this work, we…
We perform a perturbative analysis of the Aharonov-Bohm problem to one loop in a field-theoretic formulation, and show that contact interactions are necessary for renormalizability. In general, the classical scale invariance of this problem…
We investigate the gravitational Aharonov-Bohm effect, by placing a quantum system in free-fall around a gravitating body {\it e.g.} a satellite orbiting the Earth. Since the system is in free-fall, by the equivalence principle, the quantum…
Resorting to a Gedankenexperiment which is very similar to the famous Aharonov-Bohm proposal it will be shown that, in the case of a Minkowskian spacetime, we may use a nonrelativistic quantum particle and a noninertial coordinate system…
For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Starting with the overall wave function expression for the electron in an Aharonov-Bohm potential, we derive a version of the Kuramoto Model describing the phase dynamics of the bound state of the quantum mechanical system.
We propose a method called `coherence swapping' which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiations. This phenomenon is also present for the charged…
Quantum-mechanical theory for scattering of nonrelativistic charged particles with spin by a penetrable magnetic vortex is elaborated. The scattering differential cross section is shown to consist of two terms, one describing diffraction on…
We study a class of degenerate hyperbolic equations in a bounded domain whose degeneracy occurs at a boundary point. We first develop the weighted functional framework, prove well-posedness of the degenerate problem, and establish…
The aim of this article is to investigate the uniqueness of solution of an inverse problem for ultrahyperbolic equations. We first reduce the inverse problem to a Cauchy problem for an integro-differential equation and then by using a…
It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm…
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…