arXiv subjects

R. Mosseri

Publications and source records attributed to R. Mosseri.

26 records · Page 2Linked to original sources

arXiv2001

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussed

quant-ph↗

arXiv2001

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.

cond-mat↗

arXiv2001

How to escape Aharonov-Bohm cages ?

We study the effect of disorder and interactions on a recently proposed magnetic field induced localization mechanism. We show that both partially destroy the extreme confinement of the excitations occuring in the pure case and give rise to unusual behavior. We also point out the role of the edge states that allows for a propagation of the electrons in these systems.

cond-mat.mes-hall↗

arXiv2000

Interaction induced delocalisation for two particles in a periodic potential

We consider two interacting particles evolving in a one-dimensional periodic structure embedded in a magnetic field. We show that the strong localization induced by the magnetic field for particular values of the flux per unit cell is destroyed as soon as the particles interact. We study the spectral and the dynamical aspects of this transition.

cond-mat.str-el↗

arXiv2000

Fixed-boundary octagonal random tilings: a combinatorial approach

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus generalizing previous results on the more restricted class of codimension-one tilings. In particular this method gives access to counting formulas, which are directly related to questions of entropy in these statistical systems. Methods and tools from the field of enumerative combinatorics are used.

cond-mat.stat-mech↗

arXiv1999

Two-dimensional random tilings of large codimension: new progress

Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a $D$-dimensional space. We study the limiting case, when the quantity $D$, and therefore the number of different species of tiles, become large. We had previously demonstrated [ICQ6] that, in this limit, the thermodynamic properties of the tiling become independent of the boundary conditions. The exact value of the limiting entropy and finite $D$ corrections remain open questions. Here, we develop a mean-field theory, which uses an iterative description of the tilings based on an analogy with avoiding oriented walks on a random tiling. We compare the quantities so-obtained with numerical calculations. We also discuss the role of spatial correlations.

cond-mat.stat-mech↗

arXiv1998

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.

cond-mat.mes-hall↗

arXiv1998

Aharonov-Bohm cages in two-dimensional structures

We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This spectacular phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce the Aharonov-Bohm cages defined as the set of sites eventually visited by a wavepacket that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibits an original pulsating behaviour.

cond-mat.mes-hall↗