Quantum Interacting Particle Systems

Luigi Accardi, Sergei Vladimirovich Kozyrev

Guy Zisling, Lea Santos, Yevgeny Bar Lev

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

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.

Philip L. Bowers

Bogusław Zegarliński

F. Borgonovi, G. L. Celardo, Felix M. Izrailev +1 more

A novel approach is suggested for the statistical description of quantum systems of interacting particles. We show that the occupation numbers for single-particle states can be represented as a convolution of a classical analog of the eigenstate, with the quantum occupation number for noninteracting particles. The latter takes into account the wave function symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers n(s) can be found even for a large number of interacting particles. Using the model of interacting spins, we demonstrate that this approach gives a correct description of n(s) even in deep quantum regions with few single-particle orbitals.