Related papers: Geometry-induced Coulomb-like potential in helical…
We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle submitted an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in…
In this work, we show how Euclidean 3-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal…
In this letter we derive the Cornell confining potential in a theory of interacting Abelian gauge vector and massive Kalb-Ramond tensor. The Kalb-Ramond mass is instrumental to obtain the linear confining behavior of the potential at large…
The present work is a review of a series of papers, published in the last ten years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum…
We derive the Schr\"odinger equation for a particle confined to the surface of a normal and a binormal helical nanoribbon, obtain the quantum potentials induced by their respective curved surface geometries, and study the localized states…
After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the…
We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring…
We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal…
Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic…
This thesis investigates geometric approaches to quantum hydrodynamics (QHD) in order to develop applications in theoretical quantum chemistry. Based upon the momentum map geometric structure of QHD and the associated Lie-Poisson and…
We present exact solutions of the Schr\"odinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are…
A random set of points in Euclidean space is called `rigid' or `hyperuniform' if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points.…
The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, in the framework of non-relativistic quantum mechanics, was accomplished decades ago. This result did not take account of…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys.…
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a…
Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb…
We deform the interaction between nonrelativistic point particles on a plane and a Chern-Simons field to obtain an action invariant with respect to time-dependent area-preserving diffeomorphisms. The deformed and undeformed Lagrangians are…