Dresden 2020 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 39: Quantum Chaos (joint session DY/TT)

DY 39.6: Vortrag

Mittwoch, 18. März 2020, 16:30–16:45, HÜL 186

Many-Body Densities of States on Quantum Graphs — •Adrian Seith1, Gregor Tanner2, Stephen Creagh2, Klaus Richter1, and Juan-Diego Urbina11Institut für Theoretische Physik, Universität Regensburg, Universitätsstraße 31 D-93053 Regensburg — 2School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

We study the bulk density of states in non-interacting many-body systems on a quantum graph, a one-dimensional network of connected bonds on which the wave function is a solution of the one-dimensional Schrödinger equation.

In [1], Kottos & Smilansky derived a trace formula for the spectrum of a one-particle quantum graph using a secular equation and a transfer operator that describes the dynamics of the system. In [2], Bolte & Kerner show that the DOS of a many-body quantum graph follows an asymptotic Weyl law. We derive an explicit expression of the many-particle DOS on quantum graphs for distinguishable and indistinguishable particles and extend Smilansky's transfer operator approach to many-body systems using Bogomolny's formalism [3] so that we can give a geometric interpretation of many-body quantum graphs and the principle of indistinguishability and pave the way to include interaction effects.

[1] T. Kottos, U. Smilansky. Annals of Physics, Vol. 274 (1999)

[2] J. Bolte, J. Kerner. Journal of Mathematical Physics 55, (2014)

[3] E. B. Bogomolny. Nonlinearity, Vol. 5 (1992)

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