arXiv subjects

Jean Bellissard

Publications and source records attributed to Jean Bellissard.

21 records · Page 2Linked to original sources

arXiv1996

Two interacting Hofstadter butterflies

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on non commutative geometry techniques permits to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction.

cond-mat↗

arXiv1996

Double butterfly spectrum for two interacting particles in the Harper model

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.

cond-mat↗

arXiv1993

Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian

We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at points corresponding to models known to be exactly integrable Poisson statistics are found, in agreement with an argument we outline.

cond-mat↗