2015/10/01 by Andrzej Syrwid, Syrwid, Andrzej
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum optics and atomic interactions #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1510.00257
94 pages, 27 figures
arxiv created 2015/10/01 · openalex publication_date 2015/10/01 · arxiv updated 2015/10/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The thesis contains description of the Lieb-Liniger model in the context of the correspondence between dark solitons and the so-called hole excitations. We present a detailed analysis of the analytical solution given by the Bethe ansatz and discuss two types of elementary - particle (type I) and hole (type II) - excitations. It turns out that the type I excitations are reproduced by the Bogoliubov spectrum which means that they correspond to the sound waves in the system. It is believed that the eigenstates corresponding to the second branch are strictly connected with dark solitons. The main evidence bases on the comparison between the spectrum of the hole excitations and the dispersion relation of the semi-classical soliton. All the knowledge needed to fully understand the problem is presented in details in the thesis. Our numerical simulations show that successive measurement of particle positions is able to break the translation symmetry of the system and reveal particle densities expected from the dark soliton profiles if the system is prepared in a type II eigenstate. We analyze single and double dark solitons in weak and strong interaction regime.