2009/02/28 by Emerson Sadurni, E Sadurní, Juan Mauricio Torres +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Class (philosophy) #Dirac (video compression format) #Exact solutions in general relativity #Field (mathematics) #Hamiltonian (control theory) #Integrable system #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/43/28/285204
published as J. Phys. A 43:285204, 2010 · 20 pages, 1 figure. Published in JPA
openalex publication_date 2010/06/14 · arxiv created 2010/06/15 · arxiv updated 2015/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes 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 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 an example we apply this exact solution to calculate the evolution of entanglement.