DiracConf_CMPfinal.pdf (469.5 kB)
Download file

Essential Self-adjointness of Symmetric First-Order Differential Systems and Confinement of Dirac Particles on Bounded Domains in Rd

Download (469.5 kB)
journal contribution
posted on 06.04.2022, 17:33 by Gheorghe Nenciu, Irina NenciuIrina Nenciu, Ryan Obermeyer
We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary ∂Ω of the spatial domain Ω ⊂ Rd. On the way, we first consider general symmetric first order differential systems, for which we identify a new, large class of potentials, called scalar potentials, ensuring essential self-adjointness. Furthermore, using the supersymmetric structure of the Dirac operator in the two dimensional case, we prove confinement of Dirac particles, i.e. essential self-adjointness of the operator, solely by magnetic fields B assumed to grow, near ∂Ω , faster than 1 / (2 dist (x, ∂Ω) 2).

Funding

CAREER: Long-Time Asymptotics Of Completely Integrable Systems With Connections To Random Matrices And Partial Differentia Equations | Funder: National Science Foundation | Grant ID: DMS-1150427

CAREER: Adiabatic Theory for Nonlinear Schrodinger Equations with Applications in Complex Quantum Systems | Funder: National Science Foundation | Grant ID: DMS-1348092

History

Citation

Nenciu, G., Nenciu, I.Obermeyer, R. (2021). Essential Self-adjointness of Symmetric First-Order Differential Systems and Confinement of Dirac Particles on Bounded Domains in Rd. Communications in Mathematical Physics, 387(1), 361-395. https://doi.org/10.1007/s00220-021-04129-4

Publisher

Springer Science and Business Media LLC

Language

en

issn

0010-3616