108 research outputs found
Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
It has been recently found that the equations of motion of several
semiclassical systems must take into account terms arising from Berry phases
contributions. Those terms are responsible for the spin Hall effect in
semiconductor as well as the Magnus effect of light propagating in
inhomogeneous media. Intensive ongoing research on this subject seems to
indicate that a broad class of quantum systems may be affected by Berry phase
terms. It is therefore important to find a general procedure allowing for the
determination of semiclassical Hamiltonian with Berry Phase corrections. This
article presents a general diagonalization method at order for a large
class of quantum Hamiltonians directly inducing Berry phase corrections. As a
consequence, Berry phase terms on both coordinates and momentum operators
naturally arise during the diagonalization procedure. This leads to new
equations of motion for a wide class of semiclassical system. As physical
applications we consider here a Dirac particle in an electromagnetic or static
gravitational field, and the propagation of a Bloch electrons in an external
electromagnetic field.Comment: 15 page
Optimisation des phases de vol pour un drone capable de vol stationnaire et de vol en translation rapide
Les travaux présentés dans ce papier reprennent l'ensemble des aspects abordés lors de l'automatisation d'un système qui se veut être autonome : la modélisation, la linéarisation, la synthèse de loi de commande, la simulation, le pilotage, le guidage et l'optimisation. Le support expérimental est un micro-drone dont le domaine de vol est élargi(de la capacité de vol stationnaire "comme un hélicoptère" au vol d’avancement rapide "comme un avion"). Les points abordés ici sont plus particulièrement, la modélisation, la linéarisation, le pilote pour le vol stationnaire et le pilote longitudinal pour les transitions de phases de vol autonomes effectuées par séquencement de gains. Nous indiquerons également la structure du simulateur complet non linéaire qui permet de tester les lois réalisées avant de les embarquer. A la fin de l'article, les perspectives et la suite des travaux seront présentées
Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
The semiclassical limit for Dirac particles interacting with a static
gravitational field is investigated. A Foldy-Wouthuysen transformation which
diagonalizes at the semiclassical order the Dirac equation for an arbitrary
static spacetime metric is realized. In this representation the Hamiltonian
provides for a coupling between spin and gravity through the torsion of the
gravitational field. In the specific case of a symmetric gravitational field we
retrieve the Hamiltonian previously found by other authors. But our formalism
provides for another effect, namely, the spin hall effect, which was not
predicted before in this context
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
We consider the Doubly Special Relativity (DSR) generalization of Dirac
equation in an external potential in the Magueijo-Smolin base. The particles
obey a modified energy-momentum dispersion relation. The semiclassical
diagonalization of the Dirac Hamiltonian reveals the intrinsic Berry phase
effects in the particle dynamics
Inverse problem and Bertrand's theorem
The Bertrand's theorem can be formulated as the solution of an inverse
problem for a classical unidimensional motion. We show that the solutions of
these problems, if restricted to a given class, can be obtained by solving a
numerical equation. This permit a particulary compact and elegant proof of
Bertrand's theorem.Comment: 11 pages, 3 figure
Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
To build genuine generators of the rotations group in noncommutative quantum
mechanics, we show that it is necessary to extend the noncommutative parameter
to a field operator, which one proves to be only momentum dependent.
We find consequently that this field must be obligatorily a dual Dirac monopole
in momentum space. Recent experiments in the context of the anomalous Hall
effect provide for a monopole in the crystal momentum space. We suggest a
connection between the noncommutative field and the Berry curvature in momentum
space which is at the origine of the anomalous Hall effect.Comment: 4 page
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