Physics Department seminar
DIPARTIMENTO DI FISICA, VIA CELORIA 16, MILANO
AULA A in presence and streaming
https://fisica-unimi.zoom.us/my/aula.a?pwd=YzZZUUloL3hjZHIzNnBwTnBvSXhJZz09
12 Maggio 2023 – 14:30
Sergei Nechaev
LPTMS, CNRS and University Paris-Saclay, France
Devil’s staircase and modular invariance: from spectral statistics of random operators to
phyllotaxis and the Hubbard model on a ring.

We discuss the spectral statistics of the 1D Anderson-like model with random hopping,
paying attention to its relationship with some number-theoretic properties of the
Riemann-Thomae function and the Dedekind eta-function. We introduce the generalized
Riemann-Thomae function and discuss its appearance in the problem of the repulsive
particles packing on the cylinder. Also we show that the integral of the generalized
Riemann-Thomae function exhibits the Devil's staircase structure and coincides with the
ground state of the Hubbard system of particles on a ring interacting with various long-
ranged potentials.

Students are cordially invited

Contact Marco.Gherardi@unimi.it

Poster