Seeing zeros of random polynomials: quantized vortices in the ideal Bose gas

TL;DR

This paper proposes an experimental setup using a rotating Bose gas to observe the distribution of zeros of random polynomials, linking vortex positions to polynomial zeros through thermal fluctuations.

Contribution

It introduces a novel physical system to experimentally study the distribution of zeros of random polynomials via vortex observations in a Bose gas.

Findings

Vortices in the Bose gas correspond to zeros of random polynomials.

Thermal fluctuations induce randomness in vortex positions.

Density profiles reveal the distribution of polynomial zeros.

Abstract

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.