arXiv subjects

Gabriela Murguia

Publications and source records attributed to Gabriela Murguia.

6 recordsLinked to original sources

arXiv2010

Magnetic Edge States in Graphene

Magnetic confinement in graphene has been of recent and growing interest because its potential applications in nanotechnology. In particular, the observation of the so called magnetic edge states in graphene has opened the possibility to deepen into the generation of spin currents and its applications in spintronics. We study the magnetic edge states of quasi-particles arising in graphene monolayers due to an inhomogeneous magnetic field of a magnetic barrier in the formalism of the two-dimensional massless Dirac equation. We also show how the solutions of such states in each of both triangular sublattices of the graphene are related through a supersymmetric transformation in the quantum mechanical sense.

cond-mat.mes-hall↗

arXiv2010

Free Form of the Foldy-Wouthuysen Transformation in External Electromagnetic Fields

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator $(γ\cdot Π)^2$, with $Π^μ= p^μ- e A^μ$. In this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.

math-ph↗

arXiv2009

The Electron Propagator in External Electromagnetic Fields in Lower Dimensions

We study the electron propagator in quantum electrodynamics in lower dimensions. In the case of free electrons, it is well known that the propagator in momentum space takes the simple form $S_F(p)=1/(γ\cdot p-m)$. In the presence of external electromagnetic fields, electron asymptotic states are no longer plane-waves, and hence the propagator in the basis of momentum eigenstates has a more intricate form. Nevertheless, in the basis of the eigenfunctions of the operator $(γ\cdot Π)^2$, where $Π_μ$ is the canonical momentum operator, it acquires the free form $S_F(p)=1/(γ\cdot \bar{p}-m)$ where $\bar{p}_μ$ depends on the dynamical quantum numbers. We construct the electron propagator in the basis of the $(γ\cdot Π)^2$ eigenfunctions. In the (2+1)-dimensional case, we obtain it in an irreducible representation of the Clifford algebra incorporating to all orders the effects of a magnetic field of arbitrary spatial shape pointing perpendicularly to the plane of motion of the electrons. Such an exercise is of relevance in graphene in the massless limit. The specific examples considered include the uniform magnetic field and the exponentially damped static magnetic field. We further consider the electron propagator for the massive Schwinger model incorporating the effects of a constant electric field to all orders within this framework.

hep-th↗

arXiv2009

Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.

quant-ph↗

arXiv2004

Quantum versus classical scattering of Dirac particles by a solenoidal magnetic field and the correspondence principle

We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The classical limit of the perturbative quantum expressions, understood as the Planck's limit (making $\hbar$ going to zero) is analyzed and compared with the classical result. The classical cross section shows a general non-symmetric behavior with respect to the scattering angle in contradistinction to the quantum calculations performed so far. The various regimes analyzed show that the quantum cross sections do not satisfy the correspondence principle: they do not reduce to the classical result in any considered limit, an argument in favor of the interpretation of the process as a purely quantum phenomenon. We conclude that in order to restore the classical correspondence of the phenomenon, a complete non-perturbative quantum calculation for a finite solenoid radius is required.

quant-ph↗

arXiv2002

Quantum effects in the scattering by the magnetic field of a solenoid

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.

physics.class-ph↗