Topological swimming in a quantum sea

TL;DR

This paper introduces a quantum theory of swimming where small swimmers in a quantum medium can move in a topologically quantized manner, covering discrete distances without dissipation, based on quantum pump principles.

Contribution

It develops a quantum swimming equation and reveals topological quantization of swimming distances in a Fermi gas at zero temperature.

Findings

Swimming distance is quantized in half-integer multiples of the Fermi wavelength.

Swimming can occur without dissipation.

The theory is based on quantum pump results.

Abstract

We propose a quantum theory of swimming for swimmers that are small relative to the coherence length of the medium. The quantum swimming equation is derived from known results on quantum pumps. For a one-dimensional Fermi gas at zero temperature we find that swimming is topological: The distance covered in one swimming stroke is quantized in half integer multiples of the Fermi wave length. Moreover, one can swim without dissipation.