Jan 23, 2024

Logarithmically enhanced area-laws for fermions in vanishing magnetic fields in dimension two

Mathphys Analysis Seminar

Date: January 23, 2024 | 4:15 pm – 5:15 pm
Speaker: Paul Pfeiffer, FernUni Hagen
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Language: English

We consider Szegö type asymptotics (which depend on scaling a two-dimensional domain by the factor L) for the free Fermi gas subject to a constant magnetic field (Landau Hamiltonian in dimension two). For a fixed magnetic field strength B>0, these asymptotics  are known. Here, the expression grows (to leading order) with the surface area of the domain, the so-called area law. For the case B=0, there is a logarithmic enhancement with an ln(L) factor. We (almost) show a continuous transition between these two cases, if we let B tend to zero and L tend to infinity simultaneously. If B tends to zero very fast, we only see the contribution of the case B=0, while a slower vanishing magnetic field yields a logarithmic growth in B. This is based on joint work with my PhD advisor Wolfgang Spitzer.