Two-dimensional Dirac matter in the semiclassical regime
- URL: http://arxiv.org/abs/2111.11496v1
- Date: Mon, 22 Nov 2021 19:42:55 GMT
- Title: Two-dimensional Dirac matter in the semiclassical regime
- Authors: F. Fillion-Gourdeau, E. Lorin and S. Maclean
- Abstract summary: The semiclassical regime of 2D static Dirac matter is obtained from the Dirac equation in curved space-time.
An effective graded index of refraction is defined and is directly linked to the metric component in isothermal coordinates.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The semiclassical regime of 2D static Dirac matter is obtained from the Dirac
equation in curved space-time. To simplify the formulation, the Cartesian
space-time geometry parametrization is transformed to isothermal coordinates
using quasi-conformal transformations. Using this framework, it is demonstrated
that to first order, the semiclassical approximation yields the relativistic
Lorentz force equation with additional fictitious forces related to the space
curvature and to the mass gradient. An effective graded index of refraction is
defined and is directly linked to the metric component in isothermal
coordinates. Semiclassical trajectories are evaluated in a simple example by
solving the equation of motion and the Beltrami equation numerically.
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