BEC of Interacting Particles

Novikov, Alexey, Ovchinnikov, Mikhail

The motion of single quantum particle through Bose-Einstein condensate (BEC) is considered within perturbation theory with respect to the particle-BEC interaction. The Hamiltonian of BEC is diagonalized by means of Bogoliubov's method. The process of dissipation due to the creation of excitation in BEC is analyzed and the dissipation rate is calculated in the lowest order of perturbation theory. The Landau's criterion for energy dissipation in BEC is then recovered. The energy spectrum of the impurity particle due to the interaction with BEC and its effective mass are evaluated.

George D. J. Phillies

Keith R. Burnett, Stephen U. S. Choi, Matthew J. Davis +3 more

Shohei Watabe

We investigate multiparticle excitation effect on a collective density excitation as well as a single-particle excitation in a weakly interacting Bose-Einstein condensate (BEC). We find that although the weakly interacting BEC offers weak multiparticle excitation spectrum at low temperatures, this multiparticle excitation effect may not remain hidden, but emerges as bimodality in the density response function through the single-particle excitation. Identification of spectra in the BEC between the single-particle excitation and the density excitation is also assessed at nonzero temperatures, which has been known to be unique nature in the BEC at absolute zero temperature.

Joachim Kerner

In this thesis, we discuss many-particle systems on general compact quantum graphs. The results cover systems of distinguishable particles as well as systems of bosons or fermions. The main focus lies on the introduction of many-particle interactions in order to establish a useful model regarding many-particle quantum chaos 811d onc-dimensional Bose-Einstein condensation (BEC). Using suitable quadratic forms, we will characterise self-adjoint realisations of the two- and many-particle Laplacian which incorporate two different types of interactions, i.e. singular interactions localised at the vertices of the graph and contact interactions which are also present along the edges. In that context, we will establish regularity results in order to characteristic the domains of the self-adjoint realisations explicitly. We will also discuss spectral properties of the constructed operators by establishing discreteness of their spectra and Weyl laws for the corresponding eigenvalue counts. Finally, based on the introduced models of interacting particles, we discuss BoseEinstein condensation on general quantum graphs. We will distinguish between systems of bosons for which BEC occurs and such for which no BEC is present at any finite temperature. As a final result, we prove that no Bose-Einstein condensation occurs (in the sense of phase transitions) in a system of bosons interacting via repulsive hard-core interactions.

Wolfgang Nolting