Many-particle quantum hydrodynamics: Exact equations and pressure tensors

Kinetic Equations for Quantum Many-Particle Systems

One particle equations for many particle quantum systems : the MCTHDF method

This contribution is devoted to the mathematical analysis of more or less sophisticated approximations of the time evolution of systems of N quantum particles. New results for the Multiconfiguration Time Dependent Hartree Fock (MCTDHF) method (which cover the material of the talk given by the first author at the “Non linear waves conference in honor of Walter Strauss”) are summarized and compar...

Exact solutions of the equations of relativistic hydrodynamics

We use a connection between relativistic hydrodynamics and scalar field theory to generate analytic solutions describing non-stationary non-homogeneous flows of the relativistic perfect fluid with barotropic equation of state (EOS). For linear EOS p = κε we obtain selfsimilar solutions in case of plane, cylindrical and spherical symmetries. Besides, in case of extremely stiff EOS (p = ε) we obt...

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...

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 ...