2007/11/30 by Karl‐Fredrik Berggren, K. -F. Berggren, D. N. Maksimov +9
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #Scientific Research and Discoveries #cond-mat.mes-hall
paper · pdf · doi:10.1103/physreve.77.066209
published as PRE 77, 066209 (2008) · 11 pages, 14 figures
openalex publication_date 2008/06/12 · arxiv created 2008/08/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor Talphabeta(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 psi=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 Talphabeta . 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 Talphabeta(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.