1304.0889 (Jiří Minář et al.)

Dirac fields in curved spacetime as Fermi-Hubbard model with non unitary
tunnelings    [PDF]

Jiří Minář, Benoît Grémaud

In this letter we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling matrices in terms of the metric tensor. In a simple case of a static diagonal metric, the tunnelings become unitary. Alternative interpretation of the Fermi-Hubbard Hamiltonian is that of a Pauli Hamiltonian, i.e. a non relativistic limit of the Dirac Hamiltonian. In this case the tunnelings remain, in general, non unitary even for the static diagonal metric. We discuss a possibility of synthesizing such Hamiltonians by means of laser assisted tunnelings in cold atomic experiments.

View original: http://arxiv.org/abs/1304.0889