Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces

New quantum numbers for the Dirac equation in curved spacetime

We show that, on spacetimes which admit Yano tensors, it is possible to construct operators that (anti)commute with the Dirac operator, thus providing extra quantum numbers even when isometries are not present. This is the main result obtained and is valid for Yano tensors of arbitrary rank. It implies that the theory of the spinning particle in such spacetimes has no anomalies and admits genui...

Krylov subspace methods for the Dirac equation

The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the Lanczos alg...

Relativistic Photoionization Computations with the Time Dependent Dirac Equation

A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime

We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for the (linear) Dirac equation with a dimensionless parameter ε ∈ (0, 1] which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e., 0 < ε 1, the solution exhibits highly oscillatory propagating waves with wavelength O(ε2) and O(1) in time and space, resp...

Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime

In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are ...