Search results for "pseudo-boson"
showing 8 items of 38 documents
Generalized Heisenberg algebra and (non linear) pseudo-bosons
2018
We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.
Coupled Susy, pseudo-bosons and a deformed su(1, 1) Lie algebra
2021
Abstract In a recent paper a pair of operators a and b satisfying the equations a † a = bb † + γ 1 and aa † = b † b + δ 1 , has been considered, and their nature of ladder operators has been deduced and analyzed. Here, motivated by the spreading interest in non self-adjoint operators in quantum mechanics, we extend this situation to a set of four operators, c, d, r and s, satisfying dc = rs + γ 1 and cd = sr + δ 1 , and we show that they are also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called D -pseudo bosons. Some examples are discussed.
Non linear pseudo-bosons versus hidden Hermiticity
2011
The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear pseudo-bosons}. The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.
Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
2012
Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded metric in the Hilbert space of states.
Abstract ladder operators and their applications
2021
We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from this formula. Then we extend it in two ways: first we replace the original equality with formula $[H_0,Z]=\lambda Z[Z^\dagger, Z]$, and secondly we consider $[H,Z]=\lambda Z$ for some $\lambda\in\mathbb{C}$, $H\neq H^\dagger$. In both cases many applications are discussed. In particular we consider factorizable Hamiltonians and Hamiltonians written in terms of operators satisfying the generalized Heisenberg algebra or the $\D$ pseudo-bosonic commutation r…
MR3535311 Reviewed Inoue, H.(J-KYUSGM); Takakura, M.(J-FUE-AM) Regular biorthogonal pairs and pseudo-bosonic operators. (English summary) J. Math. Ph…
2017
Given a pair of operators a and b acting on a Hilbert space H, such that [a,b]=1, the authors give a method to construct a regular bi-orthogonal pair of sequences in H. They study the relationship between the conditions on a,b,a†,b† and the operators Ae,Be,A†e,B†e, considered by one of the authors in a previous paper, in the set-up of a general theory of bi-orthogonal pair sequences. Then they give a method to construct operators A and B with the so-called D-pseudo bosons conditions, i.e. the commutation rule and some assumptions, on a dense subspace D of H, considered in the literature. Finally, some physical examples are given.
More mathematics on pseudo-bosons
2013
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. We also briefly extend the results to the so-called nonlinear pseudo-bosons.
Pseudo-bosons, so far
2011
In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called pseudo-bosons. They arise from a special deformation of the canonical commutation relation [a,a †]= ll, which is replaced by [a,b]=ll, with b not necessarily equal to a †. We start discussing some of their mathematical properties and then we discuss several examples.