# Deformed quons and bi-coherent states

## TL;DR

This paper explores deformations of q-mutation relations leading to pseudo-quons and bi-coherent states, revealing their properties and potential applications in pseudo-hermitian quantum mechanics.

## Contribution

It introduces a new class of bi-coherent states for pseudo-quons, extending the understanding of deformed algebraic structures in quantum mechanics.

## Key findings

- Bi-coherent states share properties with ordinary coherent states.
- Conditions for existence and eigenstate properties of these states are established.
- Two detailed examples demonstrate the theory's applicability.

## Abstract

We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to $\D$-pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discussed in details, one connected to an unbounded similarity map, and the other to a bounded map.