Catégorie : Collaborations

Richard Legras 1 Yohann Benard 2 Hélène Rouger 2
1 LuMIn – Laboratoire Lumière, Matière et Interfaces
2 LAC – Laboratoire Aimé Cotton

Yohann Benard 1 Norberto Lopez-Gil Richard Legras 2
1 LAC – Laboratoire Aimé Cotton
2 LuMIn – Laboratoire Lumière, Matière et Interfaces

Hélène Rouger 1 Yohann Benard 1 Damien Gatinel 2 Richard Legras 3
1 LAC – Laboratoire Aimé Cotton
2 Service d’ophtalmologie [Hopital Bichat – Paris]
3 LuMIn – Laboratoire Lumière, Matière et Interfaces

Abstract : The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0,L] is derived. Our method relies on the eigenvalues distributions (extreme value statistics problem) which are explicitly obtained. The well-known Dyson singularity \sim-L/|epsilon|ln^3|\epsilon| is recovered above the crossover energy epsilon_c\sim exp-sqrt{L}. Below epsilon_c we find a log-normal suppression of the average DoS \sim 1/(|epsilon|sqrt(L))exp(-(ln^2|epsilon|)/L).

Christophe Texier 1, 2 Christian Hagendorf 3
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides
3 LPTENS – Laboratoire de Physique Théorique de l’ENS [École Normale Supérieure]

Abstract : To every product of 2×22×2 matrices, there corresponds a one-dimensional Schr\ »{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in SL(2,R)SL(2,R). We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.

Alain Comtet 1, 2 Christophe Texier 2, 3 Yves Tourigny 4
1 IHP – Institut Henri Poincaré
2 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
3 LPS – Laboratoire de Physique des Solides
4 School of Mathematics [Bristol]

Abstract : Several general results for the spectral determinant of the Schrödinger operator on metric graphs are reviewed. Then, a simple derivation for the ζζ-regularised spectral determinant is proposed, based on the Roth trace formula. Two types of boundary conditions are studied: functions continuous at the vertices and functions whose derivative is continuous at the vertices. The ζζ-regularised spectral determinant of the Schrödinger operator acting on functions with the most general boundary conditions is conjectured in conclusion. The relation to the Ihara, Bass and Bartholdi formulae obtained for combinatorial graphs is also discussed.

Christophe Texier 1, 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : High-resolution coherent X-ray diffraction experiment has been performed on the Charge-Density Wave (CDW) system K0.3MoO3K0.3MoO3. The 2kF2kF satellite reflection associated with the CDW has been measured with respect to external dc currents. In the sliding regime, the 2kF2kF satellite reflection displays secondary satellites along the chain axis which corresponds to correlations up to the micrometer scale. This super long range order is 1500 times larger than the CDW period itself.

Vincent Jacques 1 David Le Bolloc’H 2 N. Kirova 2 Sylvain Ravy 3 Jean Dumas 4
1 LAC – Laboratoire Aimé Cotton
2 LPS – Laboratoire de Physique des Solides
3 SSOLEIL – Synchrotron SOLEIL
4 MagSup – Magnétisme et Supraconductivité
NEEL – Institut Néel

Abstract : We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that the proposed scheme allows for a unification of both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

N. Regnault 1 M. O. Goerbig 2 Th. Jolicoeur 3
1 LPA – Laboratoire Pierre Aigrain
2 LPS – Laboratoire de Physique des Solides
3 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques

Abstract : We study theoretically the effects of impurities and of gap distortions in binding and self-trapping of particles added or excited over the insulating state of an antiferromagnetic Mott insulator. Wave functions of single particles or of bound excitons are affected by interactions with collective degrees of freedom, as shown by ARPES and optics experiments. The resulting self-localized state lowers the total particle energy, enhances its effective mass and splits off the electronic level below the nominal insulating gap. Most of the features measured experimentally in lightly n-doped cuprates are related to electronic states originated by anti-nodal points (π,0) of the Brillouin zone. In these points the van Hove singularity plays a major role by enhancing bound states of the electron with neutral and charged impurities and of inter-gap excitons.

A. Rojo-Bravo 1, 2 S. Brazovskii 1
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides

Abstract : We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length LφLφ is small or large compared to the perimeter LL of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than LL, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time τφτφ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.

Christophe Texier 1, 2 Pierre Delplace 2 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides