Planar Dirac electron in Coulomb and magnetic fields

Planar Dirac Electron in Coulomb and Magnetic Fields: a Bethe ansatz approach

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum was previously solved from the recursion relations. In this work we present a purely algebraic solution based on the Bethe ansatz equations. It is realised that, unlike the corresponding probl...

Quasi-exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra sl(2) which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly ...

Planar Dirac Fermions in External Electromagnetic Fields

Coulomb drag in intermediate magnetic fields

We theoretically investigated the Coulomb drag effect in coupled two-dimensional electron gases in a wide interval of magnetic field and temperature 1/t!vc!EF /\ , T!EF , t being the intralayer scattering time and vc the cyclotron frequency. We show that quantization of the electron spectrum leads to rich parametric dependences of the drag transresistance on the temperature and magnetic field. ...

Dirac neutrinos and primordial magnetic fields

We consider random primordial magnetic fields and discuss their dissipation, coherence length L0, scaling behaviour and constraints implied by the primoridal nucleosynthesis. Such magnetic fields could excite the right-helicity states of Dirac neutrinos, with adverse consequences for nucleosynthesis. We present solutions to the spin kinetic equation of a Dirac neutrino traversing a random magne...