TY - JOUR

T1 - Pairing dynamics in particle transport

AU - Scamps, Guillaume

AU - Lacroix, Denis

AU - Bertsch, G. F.

AU - Washiyama, Kouhei

PY - 2012/3/23

Y1 - 2012/3/23

N2 - We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of time-dependent Hartree-Fock (TDHF)+BCS, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in TDHF+BCS, but there are other problems with the BCS approximation that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the U and V Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schrödinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schrödinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.

AB - We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of time-dependent Hartree-Fock (TDHF)+BCS, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in TDHF+BCS, but there are other problems with the BCS approximation that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the U and V Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schrödinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schrödinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.

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U2 - 10.1103/PhysRevC.85.034328

DO - 10.1103/PhysRevC.85.034328

M3 - Article

AN - SCOPUS:84859127333

VL - 85

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 3

M1 - 034328

ER -