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

TL;DR

This paper introduces a new class of solvable Dirac oscillator models coupled to external fields, demonstrating their integrability and applying the solutions to analyze entanglement dynamics.

Contribution

It presents a novel approach to maintain solvability in Dirac oscillators with external couplings by block-diagonal Hamiltonian restructuring.

Findings

The models remain solvable with appropriate couplings.

The block-diagonal structure simplifies the solution process.

Application to entanglement evolution demonstrates practical utility.

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.