Related papers: Occurrence conditions for two-dimensional Borromea…
Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective…
When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can to a good approximation ignore the high energy states and thereby obtain…
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric…
The different kinds of behaviour of three-body systems in the weak binding limit are classified with specific attention to the transition from a true three-body system to an effective two-body system. For weakly bound Borromean systems…
We compute binding energies and root mean square radii for weakly bound systems of $N=4$ and $5$ identical bosons. Ground and first excited states of an $N$-body system appear below the threshold for binding the system with $N-1$ particles.…
During the last decades, numerous exotic states which cannot be explained by the conventional quark model have been observed in experiment. Some of them can be understood as two-body hadronic molecules, such as the famous $X(3872)$,…
Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
We investigate the formation of three-body bound states in the continuum by tracing pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a…
The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of…
We propose a method of controlling two- and three-body interactions in an ultracold Bose gas in any dimension. The method requires us to have two coupled internal single-particle states split in energy such that the upper state is occupied…
We show that some simple well studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poschl-Teller…
Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably…
We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using…
Three-body correlations in three-body exotic atoms are studied with simple models that consist of three bosons interacting through a superposition of long- and short-range potentials. We discuss the correlations among particles by comparing…
Macro properties of cold atomic gases are driven by few-body correlations, even if the gas has thousands of particles. Quantum systems composed of two and three particles with attractive zero\=/range pairwise interactions are considered for…
A description of a large system of particles is often sought in a derivation from the detailed behaviour of just a few of the particles. The present thesis deals with the connection between such microscopic features and the nature of a…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for…