Dear colleagues, for the final ITAMP lunch discussion of this semester we are happy to have Jesper Levinsen from Monach University in Melbourne as our speaker. Jesper is here the rest of the week. If you would like to meet with him, here is the link to the schedule: https://docs.google.com/spreadsheets/d/15hcUWC4JCZFbuLtyj0yYVNDGqw5Nqm0d4vD… <https://docs.google.com/spreadsheets/d/15hcUWC4JCZFbuLtyj0yYVNDGqw5Nqm0d4vD4GYbdIWc/edit?usp=sharing> Kind regards, Richard and Swati ITAMP Topical Lunch Discussion Date: Friday, May 29th Time: 12:00-1:30 pm Pizza will be served. Location: B-106 @ Center for Astrophysics (60 Garden Street) Directions: after entering the lobby of the CfA, turn right to enter the hallway of the B building. In the hallway, turn right again, and B-106 is there. Speaker: Jesper Levinsen, Monash University, Melbourne Title: Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential Abstract: The one-dimensional (1D) Fermi gas with repulsive short-range interactions provides an important model of strong correlations and is often amenable to exact methods. However, in the presence of confinement, no exact solution is known for an arbitrary number of strongly interacting fermions. Here, we propose a novel ansatz for generating the lowest-energy wavefunctions of the repulsive 1D Fermi gas in a harmonic potential near the Tonks-Girardeau limit of infinite interactions. We specialize to the case of a single impurity particle interacting with N majority particles, where we may derive analytic forms of the approximate wavefunctions. Comparing with exact numerics, we show that the overlap between the wavefunctions from our ansatz and the exact ones in the ground-state manifold exceeds 0.9997 for N<8. Moreover, the overlap for the ground-state wavefunction at strong repulsion extrapolates to ~0.9999 in the thermodynamic limit. Thus, our ansatz is essentially indistinguishable from "numerically exact" results in both the few- and many-body limits. --------------------------- Dr. Richard Schmidt Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP) Harvard-Smithsonian Center for Astrophysics MS-14 60 Garden St. Cambridge, MA 02138 U.S.A. richard.schmidt(a)cfa.harvard.edu Tel. +1 (617) 496-7610 Fax +1 (617) 496-7668