Wigner crystallization (B08)

• Subject Area: Mathematics
• Term: from 2012 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736

The emergence of crystalline order in the electron gas at low density was first predicted by Eugene Wigner in 1938 and the first direct experimental verification in an essentially 1D model system was only achieved in 2019. Our goal is an asymptotic explanation in dimension 1 and 2 of this remarkable correlation-driven phenomenon in the form that is standard in, say, sphere packing: we seek to show that, as the system size gets large, a suitable lattice achieves the best asymptotically possible energy per particle. By recent work of the proposer and coworkers, the finite low-density electron gas is known to be governed by a multi-marginal optimal transport problem, and we will combine methods from classical crystallization and optimal transport theory.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 109: Discretisation in Geometry and Dynamics
• Applicant Institution: Technische Universität Berlin
• Project Heads: Professor Dr. Marco Cicalese, until 6/2020; Professor Dr. Gero Friesecke