Band structures of hybrid graphene quantum dots with magnetic flux

Lemaalem, Bouchaib; Zahidi, Youness; Jellal, Ahmed

doi:10.1016/j.physleta.2021.127898

Cited by 1 publication

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The operators S(µ − , λ) and C(µ − , λ) are defined by power series with particular values of a n , with even and odd null coefficients, respectively. In figure 5 we represent, with solid lines, the spectrum of Hamiltonians of ( 35) and (36). We have plotted the case λ = 1 for dimension d = 6.…”

Section: Proposition 2 Hamiltonians Hmentioning

confidence: 99%

See 1 more Smart Citation

Non-standard quantum algebras and finite dimensional PT -symmetric systems

Ballesteros,

Ramírez,

Reboiro

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this work,PT-symmetric Hamiltonians defined on quantum sl(2, R) algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard Uz(sl(2,R)) Hopf algebra deformation of sl(2, R). By making use of a particular boson representation of the generators of Uz(sl(2, R)), both the co-product and the commutation relations of the quantum algebra are shown to be invariant under the PT-transformation. In terms of these operators, we construct several finite dimensional PT-symmetry Hamiltonians, whose spectrum is analytically obtained for any arbitrary dimension. In particular, we show the appearance of Exceptional Points in the space of model parameters and we discuss the behaviour of the spectrum both in the exact PT-symmetry and the broken PT-symmetry dynamical phases. As an application, we show that this non-standard quantum algebra can be used to define an effective model Hamiltonian describing accurately the experimental spectra of three-electron hybrid qubits based on asymmetric double quantum dots. Remarkably enough, in this effective model, the deformation parameter "z" has to be identified with the detuning parameter of the system.

show abstract

Section: Proposition 2 Hamiltonians Hmentioning

confidence: 99%

“…This system turns out to be the cornerstone of twodimensional (2D) semiconductor-based three-electron hybrid-double-quantum-dot (HDQD) qubits (see [19,34] and references therein). In the literature, theoretical model Hamiltonians have been developed to reproduce these experimental results [35,36].…”

Section: Applicationsmentioning

confidence: 99%