Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach

TL;DR

This paper introduces a coding method to fully describe stationary states of a one-dimensional Bose-Einstein condensate in a quasiperiodic lattice, linking solutions to bi-infinite sequences over a finite alphabet.

Contribution

It formulates conditions for a one-to-one correspondence between stationary states and symbolic sequences, enabling numerical verification and a novel coding approach.

Findings

Established sufficient conditions for coding stationary states

Demonstrated the coding approach with a three-symbol alphabet

Provided a numerical example validating the method

Abstract

We consider stationary states of an effectively one-dimensional Bose-Einstein condensate in a quasiperiodic lattice. We formulate sufficient conditions for a one-to-one correspondence between the stationary states with a fixed chemical potential and the set of bi-infinite sequences over a finite alphabet. These conditions can be checked numerically. A bi-infinite sequence can be interpreted as a code of the corresponding solution. A numerical example demonstrates the coding approach using an alphabet of three symbols.