title: Quantum stress in chaotic billiards.
abstract: This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(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 T_{alphabeta} . 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 T_{alphabeta}(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.
authors.affiliation: IFM-Theory and Modeling, Linköping University, S-581 83 Linköping, Sweden.
authors.forename: Karl-Fredrik
authors.initials: KF
authors.lastname: Berggren
authors.forename: Dmitrii N
authors.initials: DN
authors.lastname: Maksimov
authors.forename: Almas F
authors.initials: AF
authors.lastname: Sadreev
authors.forename: Ruven
authors.initials: R
authors.lastname: Höhmann
authors.forename: Ulrich
authors.initials: U
authors.lastname: Kuhl
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Stöckmann