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

Abstract

In this work, we introduce a PT-symmetric infinite-dimensional representation of the Uz(sl(2,R)) Hopf algebra, and we analyse a multiparametric family of Hamiltonians constructed from such representation of the generators of this non-standard quantum algebra. It is shown that all these Hamiltonians can be mapped to equivalent systems endowed with a position-dependent mass. From the latter presentation, it is shown how appropriate point canonical transformations can be further defined in order to transform them into Hamiltonians with constant mass over suitable domains. By following this approach, the bound-state spectrum and the corresponding eigenfunctions of the initial PT-symmetric Hamiltonians can be determined. It is worth stressing that a relevant feature of some of the new Uz(sl(2,R)) systems here presented is found to be their connection with double-well and Pöschl-Teller potentials. In fact, as an application we present a particular Hamiltonian that can be expressed as an effective double-well trigonometric potential, which is commonly used to model several relevant systems in molecular physics.

References in corpus (36)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Observation of parity-time symmetry breaking in a single spin system
• Analog gravity from Bose-Einstein condensates
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
• A systematic study on the exact solution of the position dependent mass Schroedinger equation
• Exceptional rings protected by emergent symmetry for mechanical systems
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Topological classification of defects in non-Hermitian systems
• Non-Bloch $\mathcal{P}\mathcal{T}$ symmetry breaking in non-Hermitian Photonic Quantum Walks
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with Position-Dependent Mass
• Non-Hermitian Hamiltonians of Lie algebraic type
• Universal $R$-matrix for non-standard quantum $sl(2,\mathbb{R})$
• Lie bialgebra quantizations of the oscillator algebra and their universal $R$--matrices
• Exactly solvable Schrödinger equation with double-well potential for hydrogen bond
• Analytic calculation of ground state splitting in symmetric double well potential
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Analytical solution to position dependent mass Schrödinger equation
• Analytic description of inversion vibrational mode for ammonia molecule
• The generalized Klein-Gordon oscillator with position-dependent mass in a particular Gödel-type space-time
• Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
• Boson representations, non-standard quantum algebras and contractions
• Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
• Signature of exceptional point phase transition in Hermitian systems
• Signatures of a quantum dynamical phase transition in a three-spin system in presence of a spin environment
• Analytic treatment of IR-spectroscopy data for double well potential
• Calculation of IR absorption intensities for hydrogen bond from exactly solvable Schrödinger equation
• Exceptional points of infinite order give a continuous spectrum
• Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule
• Exceptional points and pseudo-Hermiticity in real potential scattering
• Model for vibrationally enhanced tunneling of proton transfer in hydrogen bond
• Bound-states for generalized trigonometric and hyperbolic Pöschl-Teller potentials
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor