# On Thouless bandwidth formula in the Hofstadter model

## TL;DR

This paper extends the Thouless bandwidth formula to higher moments, providing a closed-form expression involving special mathematical functions, thereby deepening the understanding of spectral properties in the Hofstadter model.

## Contribution

It introduces a generalized formula for the n-th moment of the bandwidth in the Hofstadter model, expressed through polygamma, zeta, and Euler numbers.

## Key findings

- Derived a closed-form expression for the n-th moment of the bandwidth.
- Connected spectral properties to special functions like polygamma, zeta, and Euler numbers.

## Abstract

We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.