Deformed quons and bi-coherent states

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.

in press in Proceedings of the Royal Society A

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• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
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Cited by in corpus (6)

• Bi-squeezed states arising from pseudo-bosons
• Generalized Heisenberg algebra and (non linear) pseudo-bosons
• Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
• Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator
• Non-Hermitian coherent states for finite-dimensional systems
• Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators