Solution of a Hamiltonian of quantum dots with Rashba spin-orbit coupling: quasi-exact solution

Abstract

We present a method to solve the problem of Rashba spin-orbit coupling in semiconductor quantum dots, within the context of quasi-exactly solvable spectral problems. We show that the problem possesses a hidden osp(2,2) superalgebra. We constructed a general matrix whose determinant provide exact eigenvalues. Analogous mathematical structures between the Rashba and some of the other spin-boson physical systems are notified.

References in corpus (4)

• Gate control of spin dynamics in III-V semiconductor quantum dots
• Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian
• Electron spin precession in semiconductor quantum wires with Rashba spin-orbit coupling
• Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach

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• Algebraic treatments of the problems of the spin-1/2 particles in the one and two-dimensional geometry: a systematic study
• Solution of spin-boson systems in one and two-dimensional geometry via the asymptotic iteration method
• Spin Hall mode in a trapped thermal Rashba gas
• Solution of the Bosonic and Algebraic Hamiltonians by using AIM