The convergence for the Imaginary Time Step(ITS)evolution with time step is investigated by performing the ITS evolution for the Schrdinger-like equation and the charge-conjugate Schrdinger-like equation deduced from ...The convergence for the Imaginary Time Step(ITS)evolution with time step is investigated by performing the ITS evolution for the Schrdinger-like equation and the charge-conjugate Schrdinger-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 stepΔtc for a given single-particle level.The"critical"time stepΔtc is more sensitive to the quantum numbers|κ|than to the energy of the single-particle level.For the single-particle levels with the sameκ,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.展开更多
Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS)evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly boun...Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS)evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.展开更多
基金partly supported by the Major State 973 Program(Grant No.2007CB815000)the National Natural Science Foundation of China(Grant Nos.10775004 and 10975008)
文摘The convergence for the Imaginary Time Step(ITS)evolution with time step is investigated by performing the ITS evolution for the Schrdinger-like equation and the charge-conjugate Schrdinger-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 stepΔtc for a given single-particle level.The"critical"time stepΔtc is more sensitive to the quantum numbers|κ|than to the energy of the single-particle level.For the single-particle levels with the sameκ,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.
基金supported partially by Guizhou Science and Technology Foundation(Grant No J[2010]2135)the National Basic Research Program of China(Grant No 2007CB815000)the National Natural Science Foundation of China(Grant Nos 10775004,10947013,and 10975008)
文摘Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS)evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.
