Related papers: Coupling curvature to a uniform magnetic field; an…
Some relevant transport properties of solids do not depend only on the spectrum of the electronic Hamiltonian, but on finer properties preserved only by unitary equivalence, the most striking example being the conductance. When interested…
We investigate non-minimal $R^\beta F^2$-type couplings of electromagnetic fields to gravity. We derive the field equations by a first order variational principle using the method of Lagrange multipliers. Then we present various static,…
The effects of surface curvature on the motion of electrons in a mesoscopic two-dimensional ring on a cone in the presence of external magnetic fields are examined. The approach follows the thin-layer quantization procedure, which gives…
The Schr\"odinger equation for an electron under the influence of an electromagnetic field is analyzed based on the conserved operators of the system when the magnetic field is described by Landau's gauge. It is shown that the Lorentz force…
We analyze the obtained solutions of the non-linear Shroedinger equation for spherically and axially symmetrical electrons density oscillations in plasma. The conditions of the oscillations process existence are examined. It is shown that…
We present a toroidal electromagnetic ansatz that provides a realistic microscopic model of the QED electron. The proposed toroidal electromagnetic wave satisfies Maxwell's equations and reproduces fundamental properties of the electron as…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
The Hofstadter-Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moir\'e materials. Few large-scale, numerically exact simulations exists for…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
We develop a geometric formulation of thermodynamic response in the classical Ising model by defining a curvature field over the control manifold spanned by inverse temperature $\beta$ and magnetic field $h$. We show that the existence of…
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the…
A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein--Cartan theory and the possible interpretation of the torsion trace as the…
Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to the…
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of…
The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity,…
We determine the effective dynamics for a spinless charged particle, in the presence of electromagnetic fields, constrained to a space curve. We employ the thin-layer procedure and a perturbative expansion for the Schr\"odinger equation is…
Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field…
Twisted cylindrical tubes are important model systems for nanostructures, heterostructures, and curved quantum devices. In this work, we investigate the quantum behavior of an electron confined to a twisted cylindrical surface. By first…
For a harmonic map $u:M^3\to S^1$ on a closed, oriented $3$--manifold, we establish the identity $$2\pi \int_{\theta\in S^1}\chi(\Sigma_{\theta})\geq \frac{1}{2}\int_{\theta\in S^1}\int_{\Sigma_{\theta}}(|du|^{-2}|Hess(u)|^2+R_M)$$ relating…