arXiv subjects

J. V. Pulé

Publications and source records attributed to J. V. Pulé.

3 recordsLinked to original sources

arXiv2008

Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores

In this paper we study the relation between long cycles and Bose-Condensation in the Infinite range Bose-Hubbard Model with a hard core interaction. We calculate the density of particles on long cycles in the thermodynamic limit and find that the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation but this density is not equal to that of the Bose condensate.

cond-mat.stat-mech↗

arXiv2000

The Spectrum of a Magnetic Schrödinger Operator with Randomly Located Delta Impurities

We consider a single band approximation to the random Schroedinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In this paper we generalize these results by letting the delta impurites have random positions as well as strengths; they are located in squares of a lattice with a general bounded distribution. We characterize the entire spectrum of this operator when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level is infinitely degenerate and that the eigenfunctions corresponding to other Landau band energies are exponentially localized.

math-ph↗

arXiv1999

Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

We consider a random Schrodinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the lowest N Landau bands of this random Hamiltonian when the magnetic field is sufficiently strong, depending on N. We show that the spectrum in these bands is entirely pure point, that the energies coinciding with the Landau levels are infinitely degenerate and that the eigenfunctions corresponding to energies in the remainder of the spectrum are localized with a uniformly bounded localization length. By relating the Hamiltonian to a lattice operator we are able to use the Aizenman-Molchanov method to prove localization.

math-ph↗