Complex density of continuum states in resonant quantum tunneling

• URL: http://arxiv.org/abs/2002.03874v2
• Date: Wed, 17 Jun 2020 10:41:59 GMT
• Title: Complex density of continuum states in resonant quantum tunneling
• Authors: Pavel Str\'ansk\'y, Milan \v{S}indelka, Michal Kloc, and Pavel Cejnar
• Abstract summary: We show that the real part of the density is proportional to a real "time shift" of the transmitted particle, while the imaginary part reflects the imaginary time of an instanton-like tunneling trajectory. In particular, we show that stationary points of the potentials give rise to specific singularities of both real and imaginary densities which represent close analogues of excited-state quantum phase transitions in bound systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a complex-extended continuum level density and apply it to one-dimensional scattering problems involving tunneling through finite-range potentials. We show that the real part of the density is proportional to a real "time shift" of the transmitted particle, while the imaginary part reflects the imaginary time of an instanton-like tunneling trajectory. We confirm these assumptions for several potentials using the complex scaling method. In particular, we show that stationary points of the potentials give rise to specific singularities of both real and imaginary densities which represent close analogues of excited-state quantum phase transitions in bound systems.

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