Search results for "Biorthogonal system"
showing 3 items of 23 documents
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.
Gibbs states defined by biorthogonal sequences
2016
Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended version of the Heisenberg algebraic dynamics, deducing some of their properties, useful for our purposes.
Hamiltonians defined by biorthogonal sets
2017
In some recent papers, the studies on biorthogonal Riesz bases has found a renewed motivation because of their connection with pseudo-hermitian Quantum Mechanics, which deals with physical systems described by Hamiltonians which are not self-adjoint but still may have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed is some previous papers. However, in many physical models, one has to deal not with o.n. bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of $\mat…