Convergence for Imaginary Time Step evolution in the Fermi and Dirac seas

Abstract

The convergence for the Imaginary Time Step (ITS) evolution with time step is investigated by performing the ITS evolution for the Schrodinger-like equation and the charge-conjugate Schrodinger-like equation deduced from Dirac equation for the single proton levels of 12C in both the Fermi and Dirac seas. For the guaranteed convergence of the ITS evolution to the “exact” results, the time step should be smaller than a “critical” time step Δtc for a given single-particle level. The “critical” time step Δtc is more sensitive to the quantum numbers |κ| than to the energy of the single-particle level. For the single-particle levels with the same κ, their “critical” time steps are in the same order. For the single-particle levels with similar energy, a relatively small (large) “critical” time step for larger (smaller) |κ| is needed. These conclusions can be used in the future self-consistent calculation to optimize the evolution procedure.