Göttingen 2025 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 9: Poster Session: Many-body Theory
MP 9.1: Poster
Mittwoch, 2. April 2025, 16:15–18:15, ZHG Foyer 1. OG
Exact solutions of interacting spinor Bose gases — •Hannes Köper1 and Thomas Gasenzer1,2 — 1Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, D-69120 Heidelberg, Germany — 2Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
The quantum matrix non-linear Schrödinger equation in one spatial dimension describes an integrable model of two non-relativistic SU(2) multiplets with quartic interaction between their coupled states. Due to the matrix structure of the field operators involved, the non-linear term includes spin-changing processes not captured by a plain density-density interaction. In spite of the complexity of these spin changing terms for the general m × n matrix field, symmetry analysis reveals a very simple picture in terms of Casimir operators of an associated Jordan-Schwinger representation of su(n). We solve the model explicitly for the case where both multiplets are spin-1/2 giving rise to a 2 × 2 matrix field theory. The model is expected to describe e.g. the interactions between different hyperfine states in a Bose gas of hydrogen-like atoms. From its solution we derive exact thermodynamic quantities for the few- and many-body systems.
Keywords: quantum integrability; algebraic Bethe ansatz; non-linear Schrödinger equation; ultracold atoms