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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 Urbina1 — 1Institut 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)