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Physical Aspect of Exceptional Point in the Liouvillian Dynamics for a Quantum Lorentz Gas

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Non-Hermitian Hamiltonians in Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 184))

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Abstract

Physical aspect of the exceptional point in the spectrum of the Liouville-von Neumann operator (Liouvillian) is discussed. The example we study in this paper is the weakly-coupled one-dimensional quantum perfect Lorentz gas. The effective Liouvillian for the system derived by applying the Brillouin-Wigner-Feshbach formalism takes non-Hermitian form due to resonance singularity, thus its spectra take complex values. We find that the complex spectra has two second order exceptional points in the wavenumber space. As a physical effect of the exceptional points, we show that the time evolution of the Wigner distribution function is described by the telegraph equation. The time evolution described by the telegraph equation shows a shifting motion in space. We also show that mechanism of the shifting motion completely changes at the exceptional points.

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Author information

Authors and Affiliations

  1. Graduate School of Interdisciplinary Research, University of Yamanashi, Kofu, Yamanashi, 400-8511, Japan

    Kazunari Hashimoto

  2. Department of Physical Science, Osaka Prefecture University, Sakai, Osaka, 599-8531, Japan

    Kazuki Kanki & Satoshi Tanaka

  3. Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan

    Tomio Petrosky

  4. Center for Studies in Complex Quantum Systems, The University of Texas, Austin, 78712, USA

    Tomio Petrosky

Authors
  1. Kazunari Hashimoto
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  2. Kazuki Kanki
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  3. Satoshi Tanaka
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  4. Tomio Petrosky
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Corresponding author

Correspondence to Kazunari Hashimoto .

Editor information

Editors and Affiliations

  1. Dipartimento di Energia, Università degli Studi di Palermo, Palermo, Italy

    Fabio Bagarello

  2. Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, Palermo, Palermo, Italy

    Roberto Passante

  3. Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

    Camillo Trapani

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Hashimoto, K., Kanki, K., Tanaka, S., Petrosky, T. (2016). Physical Aspect of Exceptional Point in the Liouvillian Dynamics for a Quantum Lorentz Gas. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_17

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