Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

Jul 16, 2016
17 pages
Published in:
  • Annals Phys. 374 (2016) 162-178
  • Published: Nov, 2016
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Abstract: (Elsevier)
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.
Note:
  • 11 pages, 8 figures. Corrected typos
  • Optical simulation
  • Coupled waveguide array
  • Curved spacetime
  • Dirac equation
  • Particle creation
  • space-time: background
  • spinor: Dirac
  • metric: time dependence
  • black hole: horizon
  • effect: Hawking