A globally diagonalizable alpha^2-dynamo operator, SUSY QM and the Dirac equation

Abstract

A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac equation and to extract non-numerical information about the dynamo spectrum.

9 pages, 3 figures

References in corpus (4)

• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Krein space related perturbation theory for MHD alpha-2-dynamos and resonant unfolding of diabolical points
• Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
• Dynamics of charged fluids and 1/L perturbation expansions

Cited by in corpus (12)

• Making Sense of Non-Hermitian Hamiltonians
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Determining role of Krein signature for 3D Arnold tongues of oscillatory dynamos
• Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians
• Exact propagators for SUSY partners
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials
• Bound state solutions of the Klein Gordon equation with energy-dependent potentials
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• Faster than Hermitian Time Evolution
• Exactly-solvable quantum systems in terms of Lambert-W functions