A spherical-harmonic reduction turns the spectral stability of one- and bi-frequency solitary waves in the 3D Soler model into radial ODE systems, with bi-frequency waves potentially more stable.
Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski
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abstract
We consider spectral problems for many-body Dirac operators mentioned by Derezi\'{n}ski in the IAMP News Bulletin of January 2012. In particular, we derive a representation of the Dirac Coulomb operator for a helium-like ion as a matrix operator of order sixteen. We show that it is essentially self-adjoint (under natural restrictions on the coupling constants), that the essential spectrum of its closure is the whole real line and that it has no eigenvalues.
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On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D
A spherical-harmonic reduction turns the spectral stability of one- and bi-frequency solitary waves in the 3D Soler model into radial ODE systems, with bi-frequency waves potentially more stable.