Dirac-like Hamiltonians associated to Schrödinger factorizations

Plasmons due to the interplay of Dirac and Schrödinger fermions.

We study the interplay between Dirac and Schrödinger fermions in the polarization properties of a two-dimensional electron gas (2DEG). Specifically, we analyze the low-energy sector of narrow-gap semiconductors described by a two-band Kane model. In the context of quantum spin Hall insulators, particularly, in Hg(Cd)Te quantum wells, this model is named the Bernevig-Hughes-Zhang model. Interest...

Asymptotic analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson normal form

This article reviews the Birkho -Gustavson normal form theorem (BGNF) near an equilibrium point of a quantum Hamiltonian. The BGNF process is thereafter used to investigate the spectrum of Schrödinger operators in the 1:1, 1:2 and 1:3 resonances. A computer program is proposed to compute the coe cients of the BGNF up to any order.

Susy Shape-invariant Hamiltonians for the Generalized Dirac-coulomb Problem

A spin 1 2 relativistic particle described by a general potential in terms of the sum of the Coulomb potential with a Lorentz scalar potential is investigated via supersymmetry in quantum mechanics.

Semiclassical time evolution and quantum ergodicity for Dirac-Hamiltonians

Within the framework of Weyl calculus we establish a quantum-classical correspondence for the time evolution of observables generated by a Dirac-Hamiltonian. This includes a semiclassical separation of particles and antiparticles. We then prove quantum ergodicity for Dirac-Hamiltonians under the condition that a skew product of the classical relativistic translational motion and relativistic sp...

Locating the Spectrum for Magnetic Dirac and Schrödinger Operators