We study a self-adjoint realization of massless Dirac operator on bounded connected domain \Omega\subset \mathbb{R}^2 which is frequently used to model graphene. In particular, we show that this the limit, as M\to \infty , defined whole plane, with mass term size M supported outside \Omega .

Jansen and Heß – correcting an earlier paper of Douglas Kroll have derived a (pseudo-)relativistic energy expression which is very successful in describing heavy atoms. It approximate no-pair Hamiltonian the Furry picture. We show that their one-particle Coulomb case, thus resulting self-adjoint its spectrum, bounded from below for \alpha Z\leq 1.006 .

In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular the plane.We focus infinite-mass boundary condition (also called MIT bag condition).In case of bounded domains, establish asymptotic behavior low-lying (positive and negative) energies in limit strong field.Moreover, for constant B, problem half-plane find that operator has continuous spectrum except gap size 0 √ where ∈ (0, 2) is universal constant.Remarkably, characterizes certain...

We prove that the Hartree-Fock orbitals of pseudorelativistic atoms, is, atoms where kinetic energy electrons is given by operator √ -+ 1 -1, are real analytic away from origin.As a consequence, quantum mechanical ground state such never state.Our proof inspired classical analyticity nested balls Morrey and Nirenberg.However, technique has to be adapted take care nonlocal pseudodifferential operator, singularity potential at origin, nonlinear terms in equation.

We study the energy of quasi-particles in graphene within Hartree-Fock approximation. The are confined via an inhomogeneous magnetic field and interact Coulomb potential. show that associated functional has a minimizer determine stability conditions for N-particle problem such quantum dot.

This paper is devoted to semiclassical estimates of the eigenvalues Pauli operator on a bounded open set with Dirichlet conditions boundary. Assuming that magnetic field positive and few generic conditions, we establish simplicity provide accurate asymptotic involving Segal–Bargmann Hardy spaces associated field.

We consider a hydrogen-like atom in quantized electromagnetic field which is modeled by means of no-pair operator acting the positive spectral subspace free Dirac minimally coupled to vector potential. prove that infimum spectrum an evenly degenerate eigenvalue. In particular, we show bottom its strictly less than ionization threshold. These results hold true, for arbitrary values fine-structure constant and ultraviolet cut-off all Coulomb coupling constants critical one Brown-Ravenhall...

In the context of imaginary-time formalism for a scalar thermal field theory, it is shown that result performing sums over Matsubara frequencies associated with loop Feynman diagrams can be written, some classes diagrams, in terms action simple linear operator on corresponding energy integrals Euclidean theory at T=0. its simplest form referred depends only number internal propagators graph. More precisely, explicitly this \emph{thermal representation} holds two generic namely, two-vertex...

We consider a two-dimensional massless Dirac operator H in the presence of perturbed homogeneous magnetic field B=B_0+b and scalar electric potential V . For V\in L_{\rm loc}^p(\mathbb R^2) , p\in(2,\infty] b\in loc}^q(\mathbb q\in(1,\infty] both decaying at infinity, we show that states discrete spectrum are superexponentially localized. establish existence such between zeroth first Landau level assuming V=0 In addition, under condition b is rotationally symmetric satisfies certain...