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

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Abstract

The convergence for the Imaginary Time Step (ITS) evolution with time step is investigated by performing the ITS evolution for the Schrödinger-like equation and the charge-conjugate Schrödinger-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 Δt c for a given single-particle level. The “critical” time step Δt c 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.

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Authors and Affiliations

  1. Guizhou University for Nationalities, Guiyang, 550025, China

    FangQiong Li

  2. State Key Lab Nucl. Phys. & Tech., School of Physics, Peking University, Beijing, 100871, China

    Ying Zhang & Jie Meng

  3. School of Physics and Nuclear Energy Engineering, Beihang University, Beijing, 100191, China

    Jie Meng

  4. Department of Physics, University of Stellenbosch, Stellenbosch, South Africa

    Jie Meng

Authors
  1. FangQiong Li
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  2. Ying Zhang
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  3. Jie Meng
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Correspondence to Jie Meng.

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Recommended by LONG GuiLu

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Li, F., Zhang, Y. & Meng, J. Convergence for Imaginary Time Step evolution in the Fermi and Dirac seas. Sci. China Phys. Mech. Astron. 53, 327–330 (2010). https://doi.org/10.1007/s11433-010-0121-2

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  • DOI: https://doi.org/10.1007/s11433-010-0121-2

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