Quantum Lunch – University of Copenhagen

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Quantum Lunch

Speaker: Ulrich Linden, University of Stuttgart

Title: On the Fermi Polaron in Two Dimensions

Abstract: We investigate the quantum system of a Fermi gas interacting
attractively with a single impurity by contact interaction in a
two-dimensional box. The contact interaction is implemented by a
limiting procedure (resolvent limit) based on an ultraviolet
regularization. The interaction strength is fixed by the two-body
bound state energy which makes the coupling constant vanish as the
cutoff is removed.
One is interested in the ground state energy as function of the
interaction strength. There does not seem to be a closed expression
for the limiting Hamiltonian, which could be used in standard
variational principles. We establish a novel variational principle for
all negative eigenvalues of the limiting Hamiltonian, which allows to
prove that the polaron ansatz and the molecule ansatz, which are often
used in the physics literature, indeed yield upper bounds for the
ground state energy of the system.
This is joint work with Marcel Griesemer.