Some Properties of the Resonant State in Quantum Mechanics and Its Computation(Condensed Matter and Statistical Physics)

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概要

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• The resonant state of open quantum systems is studied from the viewpoint of the eigenfunction with an outgoing momentum flux. We show that the number of particles is conserved for a resonant state if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles in a fixed volume of integration would decay exponentially. Moreover, we introduce new numerical methods of treating the resonant state with the use of an effective potential. We first present a numerical method for finding a resonance pole in the complex energy plane. This method seeks an energy eigenvalue iteratively. We found that it leads to super-convergence, i.e., convergence whose rate is exponential with respect to the iteration step. Also, it is independent of the commonly used complex scaling. We also present a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Because the wave function of the resonant state is diverging away from the scattering potential, it is difficult to follow its time evolution numerically in a finite area using previous methods.

• 理論物理学刊行会の論文
• 2008-02-25

著者

• HATANO Naomichi

  Institute of Industrial Science, University of Tokyo

• PETROSKY Tomio

  Center for Complex Quantum Systems, The University of Texas at Austin

• Hatano Naomichi

  Institute Of Industrial Science The University Of Tokyo

• NAKAMURA Hiroaki

  Department of Simulation Science, National Institute for Fusion Science

• Sasada Keita

  Department Of Physics University Of Tokyo

• Petrosky Tomio

  Center For Complex Quantum Systems University Of Texas At Austin

• Petrosky Tomio

  Center For Complex Quantum Systems Department Of Physics The University Of Texas

• Nakamura Hiroaki

  Department Of Cardiology Hiratsuka Kyosai Hospital

• Nakamura Hiroaki

  Department Of Anatomy Faculty Of Medicine Saitama Medical University

• SASADA Keita

  Department of Physics, University of Tokyo

• PETROSKY Tomio

  Center for Complex Quantum Systems, University of Texas at Austin

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