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

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

2009-02-09

arxiv.org/abs/0902.1476v4

J. Phys. A 43:285204, 2010

Physics

Quantum Physics

20 pages, 1 figure. Published in JPA

Scientific paper

10.1088/1751-8113/43/28/285204

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.

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