On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

DOI10.1063/1.4826356zbMath1284.81361arXiv1304.3982OpenAlexW3103226144WikidataQ57999171 ScholiaQ57999171MaRDI QIDQ5410914

Yao-Zhong Zhang

Publication date: 17 April 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3982

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum optics (81V80) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (25)

Analytical solution and hidden symmetry operators of asymmetric two-mode quantum Rabi model ⋮ Full spectrum of the two-photon and the two-mode quantum Rabi models ⋮ On the 2-mode and k-photon quantum Rabi models ⋮ Spectral Determinant of the Two‐Photon Quantum Rabi Model ⋮ Hidden \(sl(2)\)-algebraic structure in Rabi model and its 2-photon and two-mode generalizations ⋮ Algebraic properties and spectral collapse in nonlinear quantum Rabi models ⋮ Quantum dynamics of two-photon quantum Rabi model ⋮ One-dimensional harmonic oscillator problem and its hidden \(SU(1,1)\) symmetry in the presence of a minimal length ⋮ The quantum Rabi model: solution and dynamics ⋮ Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model ⋮ Exact solution of the two-mode quantum Rabi model ⋮ Reduced density matrix and quantum correlation in two-qubit quantum Rabi model ⋮ One-dimensional quasi-exactly solvable Schrödinger equations ⋮ Haydock's recursive solution of self-adjoint problems. Discrete spectrum ⋮ \(\mathbb Z_N\) symmetric chiral Rabi model: a new \(N\)-level system ⋮ A unified treatment of polynomial solutions and constraint polynomials of the Rabi models ⋮ The asymmetric quantum Rabi model and generalised Pöschl–Teller potentials ⋮ Approximating the two-mode two-photon Rabi model ⋮ Bound states of two-photon Rabi model at the collapse point ⋮ Two-photon Rabi–Stark model ⋮ Dark-like states for the multi-qubit and multi-photon Rabi models ⋮ Level crossings and new exact solutions of the two-photon Rabi model ⋮ The Yang–Baxter paradox ⋮ Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model ⋮ Hidden symmetry in the biased Dicke model

Cites Work

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• Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
• Quasi-exactly-solvable problems and sl(2) algebra
• Exact solutions for a family of spin-boson systems
• Exact polynomial solutions of second order differential equations and their applications
• Quadratic Lie algebras and quasiexact solvability of the two-photon Rabi Hamiltonian
• On the spectrum of a two-level system
• Exact isolated solutions for the two-photon Rabi Hamiltonian
• Polynomial algebras and exact solutions of general quantum nonlinear optical models: II. Multi-mode boson systems

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