Related papers: Non-relativistic Quantum Mechanics on a Twisted Cy…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a…
We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…
We present a way to manipulate an electron trapped in a layered quantum dot based on near-threshold properties of one-body potentials. We show that potentials with a simple global parameter allows the manipulation of the wave function…
A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum…
Scattering of electrons from chiral spin textures such as the skyrmions is an emerging research area due to its richness in topological quantum transport, which is significant for spintronic devices. We study the dynamical process of…
We report elastic scattering theory for surface electron waves in quantum corrals defined by adatoms on the surface of noble metals. We develop a scattering-matrix technique that allows us to account for a realistic smooth potential profile…
The potential scattering of electrons carrying non--zero quanta of the orbital angular momentum (OAM) is studied in a framework of the generalized Born approximation, developed in our recent paper by Karlovets \textit{et al.}, Phys. Rev. A.…
In this work, we investigate the effects of a controlled conical geometry on the electric charge transport through a two-dimensional quantum ring weakly coupled to both the emitter and the collector. These mesoscopic systems are known for…
Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer…
We calculate the spatial entanglement between two electrons trapped in a nanostructure for a broad class of confinement potentials, including single and double quantum dots, and core-shell quantum dot structures. By using a parametrized…
In this paper, we investigate the influence of the geometry in the electronic states of a quantum ripple surface. We have considered an electron governed by the spinless stationary Schr\"{o}dinger equation constrained to move on the ripple…
Finite size effects alter not only the energy levels of small systems, but can also lead to new effective interactions within these systems. Here the problem of low energy quantum scattering by a spherically symmetric short range potential…
In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic…
Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly…
In this paper, we investigate the influence of the geometry in the electronic states of a quantum Beltrami surface. We have considered an electron governed by the spinless stationary Schr\"{o}dinger equation constrained to move on the…
We study the quantum dynamics of cold atoms initially confined in a Helical Optical Tube (HOT) and subsequently released into free space. This helicoidal potential, engineered via structured light fields with orbital angular momentum,…
We consider a single electron traveling along a strictly one-dimensional quantum wire interacting with another electron in a quantum ring capacitively coupled to the wire. We develop an exact numerical method for treating the scattering…