# Condensed Matter Seminar Series

## Residual Coulomb Interaction Fluctuations in Chaotic Systems: The Boundary, Random Plane Waves, and Semiclassical Theory

### Denis Ullmo

#### CNRS & Université Paris Sud, Orsay France

##### Thursday October 25, 11:30 am, Room 298, Physics Building

Abstract: New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the variation of the residual interactions contributions to quantum dots ground state energy as one particle is added to the system. Two theoretical approaches are developed for calculating such quantities, one based on a combination of semiclassical theory and random plane wave modeling, and the other on a semiclassical trace formula following the work of Bogomolny [Physica 31D, 169 (1988)]. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. An ingredient missing in the random plane wave modeling of chaotic eigenstates is identified.

*Host: Harold Baranger*