The Dirac point electron in zero-gravity Kerr--Newman spacetime

Dirac's wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr--Newman spacetime is studied in a zero-gravity limit; here, "zero-gravity" means $G\to 0$, where $G$ is Newton's constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint; the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. Some of our results extend to a generalization of the zero-$G$ Kerr--Newman spacetime with different electric-monopole-to-magnetic-dipole-moment ratio.Comment: 49 pages, 17 figures; referee's comments implemented; the endnotes in the published version appear as footnotes in this preprin

Protracted Screening in the Periodic Anderson Model

The asymmetric infinite-dimensional periodic Anderson model is examined with a quantum Monte Carlo simulation. For small conduction band filling, we find a severe reduction in the Kondo scale, compared to the impurity value, as well as protracted spin screening consistent with some recent controversial photoemission experiments. The Kondo screening drives a ferromagnetic transition when the conduction band is quarter-filled and both the RKKY and superexchange favor antiferromagnetism. We also find RKKY-driven ferromagnetic and antiferromagnetic transitions.Comment: 5 pages, LaTeX and 4 PS figure

Arrival/Detection Time of Dirac Particles in One Space Dimension

In this paper we study the arrival/detection time of Dirac particles in one space dimension. We consider particles emanating from a source point inside an interval in space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of "arrival time" or "detection time" are problematic in the orthodox narratives of quantum mechanics, since time is not a self-adjoint operator. We instead use an absorbing boundary condition proposed by Tumulka for Dirac's equation for the particle, which is meant to simulate the interaction of the particle with the detectors. By finding an explicit solution, we prove that the initial-boundary value problem for Dirac's equation satisfied by the wave function is globally well-posed, the solution is smooth, and depends smoothly on the initial data. We verify that the absorbing boundary condition gives rise to a non-negative probability density function for arrival/detection time computed from the flux of the conserved Dirac current. By contrast, the free evolution of the wave function (i.e., if no boundary condition is assumed) will not in general give rise to a nonnegative density, while Wigner's proposal for arrival time distribution fails to give a normalized density when no boundary condition is assumed. As a consistency check, we verify numerically that the arrival time statistics of Bohmian trajectories match the probability distribution for particle detection time derived from the absorbing boundary condition.Comment: 12 pages, 8 figure