Quantum stress in chaotic billiards

Karl-Fredrik Berggren, Dmitrii N. Maksimov, Almas F. Sadreev, Ruven Höhmann, Ulrich Kuhl, and Hans-Jürgen Stöckmann
Phys. Rev. E 77, 066209 – Published 12 June 2008; Erratum Phys. Rev. E 79, 019901 (2009)

Abstract

This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor Tαβ(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as ψ=u+iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components Tαβ. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for Tαβ(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

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  • Received 8 November 2007

DOI:https://doi.org/10.1103/PhysRevE.77.066209

©2008 American Physical Society

Erratum

Erratum: Quantum stress in chaotic billiards [Phys. Rev. E 77, 066209 (2008)]

Karl-Fredrik Berggren, Dmitrii N. Maksimov, Almas F. Sadreev, Ruven Höhmann, Ulrich Kuhl, and Hans-Jürgen Stöckmann
Phys. Rev. E 79, 019901 (2009)

Authors & Affiliations

Karl-Fredrik Berggren1, Dmitrii N. Maksimov2, and Almas F. Sadreev1,2

  • 1IFM–Theory and Modeling, Linköping University, S-581 83 Linköping, Sweden
  • 2L.V. Kirensky Institute of Physics, 660036, Krasnoyarsk, Russia

Ruven Höhmann, Ulrich Kuhl, and Hans-Jürgen Stöckmann

  • AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany

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Issue

Vol. 77, Iss. 6 — June 2008

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