Lévy distribution in many-particle quantum systems

Lévy distribution in many-particle quantum systems

The Lévy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grandcanonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas—a one-dimensional gas of N impenetrable (hard-core) bosons–harmonically confined on a lattice at fini...

Kinetic Equations for Quantum Many-Particle Systems

Unified theory of quantum many-particle systems

Using eigen-functional bosonization method, we study quantum manyparticle systems, and show that the quantum many-particle problems end in to solve the differential equation of the phase fields which represent the particle correlation strength. Thus, the physical properties of these systems are completely determined by the differential equation of the phase fields. We mainly focus on the study ...

Quantum many particle systems in ring-shaped optical lattices.

In the present work we demonstrate how to realize a 1D closed optical lattice experimentally, including a tunable boundary phase twist. The latter may induce "persistent currents" visible by studying the atoms' momentum distribution. We show how important phenomena in 1D physics can be studied by physical realization of systems of trapped atoms in ring-shaped optical lattices. A mixture of boso...

Quantification of correlations in quantum many-particle systems.

We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states. The usefulness of this general concept is demonstrated by quantifying correlations of interacting electrons in the Hubbard model and in a series of transition...