2013/04/30 by Jiří Minář, Benoît Grémaud · 15 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dirac (video compression format) #Dirac fermion #Fermion #Hamiltonian (control theory) #Metric (unit) #Quantum Mechanics and Non-Hermitian Physics #Quantum tunnelling #Spacetime #Topological Materials and Phenomena #Unitary state #cond-mat.quant-gas #hep-lat #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/16/165001
published in Journal of Physics A Mathematical and Theoretical 48(16), 165001 (Institute of Physics) · 9 pages, 4 figures. New results and figures added
arxiv created 2014/07/01 · openalex publication_date 2015/03/27 · arxiv updated 2015/03/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight-binding Hamiltonian with non-unitary tunneling amplitudes. We find the form of the non-unitary tunneling matrices in terms of the metric tensor. The main motivation behind this exercise is the feasibility of such Hamiltonians by means of laser-assisted tunnelings in cold atomic experiments. The mapping thus provides a physical interpretation of such Hamiltonians. We demonstrate the use of the mapping on the example of a time-dependent metric in 2+1 dimensions. Studying the spin dynamics, we find qualitative agreement with known theoretical predictions, namely particle pair creation in an expanding Universe.