QLunch: Symmetry and Combinatorics for Identical Quantum Systems – University of Copenhagen

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QMath > Events > Quantum Lunch > w 19 Nathan Harshmark

QLunch: Symmetry and Combinatorics for Identical Quantum Systems

Speaker: Nathan L. Harshman, American University (Washington, DC, USA) and Aarhus University

Title: Symmetry and Combinatorics for Identical Quantum Systems

Abstract:
Experiments with a few identical particles trapped in a few optical wells motivate the analysis of the combinatorial properties of N particles in M wells using the framework of kinematic symmetries of the Hamiltonian. These symmetries depend sensitively on the shape of the traps and the nature of the interactions. Extra combinatorial symmetries emerge in the limits of no interaction, no tunneling among wells, and hard-core interactions. Wreath products allow classification of these symmetry groups and permutation modules describe irreducible representations tailored for the description of indistinguishable particles. One possible application of this analysis is embodying difficult combinatorial problems in few-body, few-well systems and using the tunable dynamics to “solve the problem”.