arXiv subjects

Y. Georgelin

Publications and source records attributed to Y. Georgelin.

11 recordsLinked to original sources

arXiv2004

Vortex in Maxwell-Chern-Simons models coupled to external backgrounds

We consider Maxwell-Chern-Simons models involving different non-minimal coupling terms to a non relativistic massive scalar and further coupled to an external uniform background charge. We study how these models can be constrained to support static radially symmetric vortex configurations saturating the lower bound for the energy. Models involving Zeeman-type coupling support such vortices provided the potential has a "symmetry breaking" form and a relation between parameters holds. In models where minimal coupling is supplemented by magnetic and electric field dependant coupling terms, non trivial vortex configurations minimizing the energy occur only when a non linear potential is introduced. The corresponding vortices are studied numerically

cond-mat.other↗

arXiv2004

Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry II

We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the integral or fractionnal quantization of the Hall conductivity depending on the value of $NB/2π$ ($N$ is the number of charge carriers and $B$ is the magnetic field). When $NB/2π$ is irrationnal, we show that monovalued wave functions can be constructed only on the graph of a free group with two generators. When $NB/2π$ is rationnal, the relevant space becomes a puncturated Riemann surface. We finally discuss our results from a phenomenological viewpoint.

cond-mat.mes-hall↗

arXiv2003

Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry

In this paper, we revisit some quantum mechanical aspects related to the Quantum Hall Effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of Quantum Hall experiments. The resulting formalism is then used to compute explicitely the Hall conductivity from a Kubo formula.

cond-mat.mes-hall↗

arXiv2000

Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with field

We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Zn-abelian Higgs model with Chern-Simons and bare mass term.

cond-mat.mes-hall↗

arXiv1999

Visibility diagrams and experimental stripe structure in the quantum Hall effect

We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a stripe structure reproducing some of the experimental features that have been observed in the study of the quantum fluctuations of the Hall conductance. Furthermore, we exhibit new properties of the visibility diagrams stemming from the structure of subgroups of the full modular group.

cond-mat.mes-hall↗

arXiv1999

$Γ(2)$ modular symmetry, renormalization, group flow and the quantum Hall effect

We construct a family of holomorphic $β$-functions whose RG flow preserves the $Γ(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependance of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occuring in the crossover of the permitted transitions is discussed.

cond-mat.mes-hall↗

arXiv1998

Experimental evidence for a power law in electroencephalographic $α$-wave dynamics

We perform an experimental study of the time behavior of the $α$-wave events occuring in human electroencephalographic signals. We find that the fraction of the time spent in an $α$-burst of time size $τ$ exhibits a scaling behavior as a function of $τ$. The corresponding exponent is equal to 1.75$\pm$0.13. We therefore point out the existence of a new power law appearing in physiology. Furhtermore, we show that our experimental result may have a possible explanation within a class of Self-Organized Critical (SOC) models recently proposed by Boettcher and Paczuski. In particular, one of these models, when properly re-interpreted, seems to be consistent both with our result and a commonly accepted physiological description of the possible origin of $α$-wave events.

physics.bio-ph↗

arXiv1996

The group $Γ(2)$ and the fractional quantum hall effect

We analyze the action of the inhomogeneous modular group $Γ(2)$ on the three cusps of its principal fundamental domain in the Poincare half plane. From this, we obtain an exhaustive classification of the fractional quantum Hall numbers. This classification is somehow similar to the one given by Jain. We also present some resulting remarks concerning direct phase transitions between the different quantum Hall states.

cond-mat↗

arXiv1995

Linear Connections on the Two Parameter Quantum Plane

We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there exists a non trivial family of linear connections only when the two parameters obeys a specific relation.

q-alg↗

arXiv1995

On The non-commutative Riemannian geometry of GL_q(n)

A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the stability of linear connections under involution are discussed. Candidates for generalized permutation on GL_q(n) are found. It is shown that, for a given generalized permutation, there exists one and only one associated linear connection. Properties of the linear connection are discussed, in particular its bicovariance, torsion and commutative limit.

q-alg↗

arXiv1993

The No-Hair Conjecture in 2D Dilaton Supergravity

We study two dimensional dilaton gravity and supergravity following hamiltonian methods. Firstly, we consider the structure of constraints of 2D dilaton gravity and then the 2D dilaton supergravity is obtained taking the squere root of the bosonic constraints. We integrate exactly the equations of motion in both cases and we show that the solutions of the equation of motion of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity only by boundary conditions on the fermionic variables, i.e. the black holes of 2D dilaton supergravity theory are exactly the same black holes of 2D bosonic dilaton gravity modulo supersymmetry transformations. This result is the bidimensional analogue of the no-hair theorem for supergravity.

gr-qc↗