Dynamics of a Dirac oscillator coupled to an external field: A new class of solvable problems

Abstract

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the known solution of the Dirac oscillator into matrix form; there one notices, that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two-dimensional. Choosing couplings that do not affect the block structure, these just blow up the $2\times 2$ matrices to $4\times 4$ matrices, thus conserving solvability. The result can be cast again in covariant form. By way of example we apply this exact solution to calculate the evolution of entanglement.

20 pages, 1 figure. Published in JPA

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• Mapping of the 2+1 Dirac-Moshinsky Oscillator Coupled to an External Isospin Field onto Jaynes-Cummings Model
• Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Decoherence at constant excitation