Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 54: Focus Session: Many-Body Interference and Quantum Statistical Physics (joint session DY/TT)

DY 54.2: Hauptvortrag

Donnerstag, 10. März 2016, 15:30–16:00, H20

Canonical description of short-range interacting few-body quantum systems — •Quirin Hummel, Benjamin Geiger, Juan Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

The theoretical study of quantum few-body systems poses a fundamental challenge since the absence of a large number of particles makes the usually simplifying description within the grand canonical formalism invalid. We analytically address the fundamental interplay between indistinguishability, interactions and many-body interference in bosonic and fermionic systems with strictly fixed total particle number; quantum statistics is treated exactly and interparticle forces are described non-perturbatively. We perform calculations for thermodynamic and spectral quantities by expanding the canonical partition function in terms of Ursell operators in the short-time approximation where the discreteness of many-body spectra is neglected. This approach is specially suitable for the few-body case as it generates thermodynamic and spectral properties in terms of a finite set of permutation and interaction events thus overcoming the inappropriate use of virial expansions.

For 1D systems with short-range interactions we present analytical expressions applicable to both integrable prototypical systems such as the Lieb-Liniger and Gaudin-Yang models as well as realistic non-integrable models with harmonic confinement.