Moebius Schrodinger

TL;DR

This paper demonstrates that a 1D lattice Schrödinger operator with a potential based on the Moebius function exhibits positive Lyapunov exponents, highlighting the Moebius function's pseudo-random properties in quantum systems.

Contribution

It provides a novel example linking number theory and quantum physics by analyzing the spectral properties of a Schrödinger operator with Moebius-based potential.

Findings

Positive Lyapunov exponent for the operator

Supports the Moebius randomness law in quantum models

Connects number theory with spectral theory

Abstract

It is shown that the 1-dimensional lattice Schrodinger operator with potential given by a non-zero multiple of the Moebius function has positive Lyapounov exponent. In view of the classical theory of random Schrodinger operators, this may be seen as another manifestation of the Moebius randomness law.