Unique mixing of the shift on the C*--algebras generated by the q--canonical commutation relations

TL;DR

This paper proves that the shift on C*-algebras generated by the Fock representation of q-commutation relations exhibits unique mixing when |q|<1, highlighting a strong ergodic property in this quantum algebra setting.

Contribution

It establishes the unique mixing property of the shift on these C*-algebras for the first time in the context of q-commutation relations.

Findings

The shift is uniquely mixing for |q|<1.

The result applies to C*-algebras generated by Fock representations.

It demonstrates strong ergodic behavior in quantum algebra dynamics.

Abstract

The shift on the C^*--algebras generated by the Fock representation of the q--commutation relations has the strong ergodic property of unique mixing, when |q|<1.