More mathematics for pseudo-bosons

Abstract

We propose an alternative definition for pseudo-bosons. This simplifies the mathematical structure, minimizing the required assumptions. Some physical examples are discussed, as well as some mathematical results related to the biorthogonal sets arising out of our framework.

References in corpus (2)

• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Non Hermitian Operators with Real Spectrum in Quantum Mechanics

Cited by in corpus (18)

• From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
• A non self-adjoint model on a two dimensional noncommutative space with unbound metric
• Model pseudofermionic systems: connections with exceptional points
• Biorthogonal vectors, sesquilinear forms and some physical operators
• Non-self-adjoint hamiltonians defined by generalized Riesz bases
• Hamiltonians defined by biorthogonal sets
• $\mathcal{D}$-deformed harmonic oscillators
• Weak pseudo-bosons
• General theory of regular biorthogonal pairs and its physical applications
• Coherent states for graphene under the interaction of crossed electric and magnetic fields
• $\mathcal{D}$ pseudo-bosons in quantum models
• Appearances of pseudo-bosons from Black-Scholes equation
• Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene
• Semi-regular biorthogonal pairs and generalized Riesz bases
• Generalized Bogoliubov transformations versus $\mathcal{D}$% -pseudo-bosons
• Generalized Riesz systems and orthonormal sequences in Krein spaces
• Some perturbation results for quasi-bases and other sequences of vectors
• Fermionic model with a non-Hermitian Hamiltonian