Few-body approaches to one-dimensional many-body systems

Alexandre M. Zagoskin

Artem G. Volosniev

The research in this dissertation is devoted to few-body bound state physics in experimentally relevant systems of trapped atoms and molecules. First, the complexes of tubes containing dipoles are considered. The tubes are assumed to have zero width such that one-dimensional treatment can be applied. For this setup few-body bound structures are found for different polarization an- gles and dipole strengths by using stochastic variational methods. After that a similar analysis is provided for two-dimensional planes filled with dipolar par- ticles. At the end of the thesis, a system of particles in one-dimensional traps is analyzed assuming that two-body interactions are of zero range. It is shown that such a system is solvable in the limit of infinitely strong repulsion between particles.

Bo-Bo Wei

Fabian Brauneis, H.‐W. Hammer, S. M. Reimann +1 more

The authors present a benchmark study of different renormalization procedures for a one-dimensional ultracold few-body system made of a two-component fermionic mixture interacting via a delta contact potential. They find that using effective interactions and a running coupling constant instead of the bare interaction improves convergence significantly.

Amin S. Dehkharghani

In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models and numerical methods both for the few- and many-body systems. One-dimensional systems are very interesting in a sense that particles aligned on a line can only change seats by going through each other. This property can be exploited in the strongly interacting regime, where particles are forced to sit in a specific configuration, which can be easily manipulated. The knowledge of how and where the particles are can be exploited in future quantum applications. In short, the thesis is about establishing a solid knowledge about everything that one needs to know about the one-dimensional few- and many-component interacting quantum systems trapped in harmonic oscillator potentials.

Walter Greiner