Regensburg 2019 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 21: Statistical Physics (General) II
DY 21.1: Talk
Tuesday, April 2, 2019, 14:00–14:15, H6
Ground state energy of noninteracting fermions with a random energy spectrum — •Hendrik Schawe1, Alexander K. Hartmann1, Satya M. Majumdar2, and Grégory Schehr2 — 1Institut für Physik, Carl von Ossietzky Universität Oldenburg — 2Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris-Sud
We study the distribution of the ground states of a toy model for K noninteracting fermions. In the spirit of Derrida’s random energy model, we assume the N energy levels εi to be independently, identically distributed according to p(ε). The ground state energy is the sum of the K smallest energy levels. While the single energy levels are independent, correlations arise due to the ordering. We derive analytically a universal form for the limit of N→∞ only dependent on the small ε behavior of p(ε), which reduces in the K=1 case to the well-known Weibull distribution. Further, we confirm this analytical limiting form with numerical data not only in the main region of the distribution but also including the very rare event tails of probabilities much smaller than 10−100. In this talk we will focus on the numerical calculations necessary to reach this precision.