Related papers: One-dimensional Coulomb problem in Dirac materials
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for…
One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation…
We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The…
We evaluate the matrix elements <Or^{p}>, where O ={1, \beta, i\alpha n \beta} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of the…
This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of…
The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac…
Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on 2D quantum problems and present complete treatment on the correspondence including the Schroedinger equation, eigenfunctions and…
We analyze the quantum dynamics of a scalar field in a spacetime incorporating dual topological defects, specifically a cosmic string and a global monopole. Utilizing a generalized metric that encapsulates the combined geometric effects of…
We investigate theoretically the ground-state configurations of two-dimensional charged-particle systems with an elliptical hard-wall boundary and their vibrational eigenmodes. The systems exhibit a series of structural transitions, finally…
Chiral anomalies resulting from the breaking of classical symmetries at the quantum level are fundamental to quantum field theory and gaining ever-growing importance in the description of topological materials in condensed matter physics.…
The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished, physically most…
On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in…
We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…
As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…