Many-Particle Quantum Systems

Mattia Walschaers

Sølve Selstø, Simen Kvaal

In numerical studies of the dynamics of unbound quantum mechanical systems, absorbing boundary conditions are frequently applied. Although this certainly provides a useful tool in facilitating the description of the system, its applications to systems consisting of more than one particle are problematic. This is due to the fact that all information about the system is lost upon the absorption of one particle; a formalism based solely on the Schrödinger equation is not able to describe the remainder of the system as particles are lost. Here we demonstrate how the dynamics of a quantum system with a given number of identical fermions may be described in a manner which allows for particle loss. A consistent formalism which incorporates the evolution of sub-systems with a reduced number of particles is constructed through the Lindblad equation. Specifically, the transition from an N -particle system to an ( N − 1)-particle system due to a complex absorbing potential is achieved by relating the Lindblad operators to annihilation operators. The method allows for a straight forward interpretation of how many constituent particles have left the system after interaction. We illustrate the formalism using one-dimensional two-particle model problems.

Albert Thomas Fromhold

Jaramillo Avila, Benjamín Raziel

This thesis deals with systems of interacting particles with very low energy in the limit where the particle-particle scattering is much larger than the range of the interactions. We use a quantum-field-theory approach which allows us to study both few-body and dense-matter systems in a unified framework. This allows to introduce composite fields of two and three particles (when appropriate). The quantum corrections are calculated nonperturbatively with the Functional RenormalisationGroup.We deal with three types of systems. First we study systems with three and four scalar particles. For three-particle systems our framework describes the Efimov effect. During the FRG flow in the scaling limit, the four-particle system has an infinite sequence of (unphysical) four-particle states on top of each Efimov trimer. This is a case of super Efimov behaviour. Three of these four-particle states survive to the physical limit. Two of these three states have been found in exact quantum-mechanical calculations, and have also been observed in gases of ultracold atoms.Next, this thesis studies systems of three and four spin-1/2 particles. In the scaling limit, we find attractive fixed points for the three- and four-particle systems. Out of the scaling limit, we study atom-molecule scattering and molecule-molecule scattering, in particular their scattering length. Finally, we study dense-matter systems of spin-1/2 particles. This calculation includes all the two-, three-, and four-particle interactions. These systems show spontaneous symmetry breaking: the two-particle field has a finite classical value. We find the value of the atom gap in units of the chemical potential.

Ajit Kumar

Tingwei Zhou

Entanglement of the wave–particle duality of particles has attracted enormous attention as one of fundamental feature of quantum mechanics. Herein, we systematically studied the wave–particle entanglement of the particle system composed of N particles. The results indicate that the particle system has the wave–particle entanglement after the interaction, when the wave function of any one of the system can be obtained by using same basis vectors before the interaction. Moreover, a construction method of the wave–particle entanglement state is found for the particle system. Finally, the photons can show the wave–particle entanglement in the previous experimental work, which was further confirmed by the construction method. The results provide a new understanding for the entanglement of the wave–particle duality.