Dynamics of a Dirac oscillator coupled to an external field: A new class of solvable problems ✩,✩✩
Emerson Sadurní, J. M. Torres A, T. H. Seligman A, Autónoma México, Morelos México · 2012
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 twodimensional. Choosing couplings that do not affect the block structure, these just blow up the 2 × 2 matrices to 4 × 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.