Related papers: Non-relativistic Quantum Mechanics on a Twisted Cy…
We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We…
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum…
The propagation of matter waves in curved geometry is relevant for electrons in nano-wires, solid-state physics structures and atomtronics. Curvature effects are usually addressed within the adiabatic limit and treated via an effective…
We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench…
Photons carrying non-zero orbital angular momentum (twisted photons) are well-known in optics. Recently, it was suggested to use Compton backscattering to boost optical twisted photons to high energies. Twisted electrons in the intermediate…
A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the…
We investigate the controllability of quantum electrons trapped in a two-dimensional device, typically a MOS field-effect transistor. The problem is modeled by the Schr\"odinger equation in a bounded domain coupled to the Poisson equation…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…
In this paper, we investigate the elastic scattering of an electron by a Yukawa potential within the framework of non-commutative (NC) geometry. We first derive the NC correction to the Yukawa potential at leading order in the NC parameter,…
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of…
This study explores the influence of a Stark-like perturbative potential on a quantum particle confined to a cylindrical surface (QPCS) and its implications for extra-dimensional theories. The QPCS framework is particularly relevant to…
In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We found the Schr\"odinger equation for a general surface following the da Costa approach,…
Devices exhibiting the integer quantum Hall effect can be modeled by one-electron Schroedinger operators describing the planar motion of an electron in a perpendicular, constant magnetic field, and under the influence of an electrostatic…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…
Circular Rydberg states offer advantages for quantum information and quantum simulation platforms due to their long lifetimes and strong dipole-dipole interactions. Unfortunately, current techniques for the production of these states remain…
Context: Due to advances in synthesizing lower dimensional materials there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently…
We study the scattering of Dirac electrons of circular graphene quantum dot with mass-inverted subject to electrostatic potential. The obtained solutions of the energy spectrum are used to determine the scattering coefficients at the…
The experimental progress in synthesizing low-dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. It was recently asserted…