Current and vortex statistics in microwave billiards

Abstract

Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system probability densities and currents were studied in a microwave billiard with a ferrite insert as well as in an open billiard. Distribution functions were obtained for probability densities, currents and vorticities. In addition the vortex pair correlation function could be extracted. For all studied quantities a complete agreement with the predictions from the random-superposition-of-plane-waves approach was obtained.

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

“…1, which is designed after a cavity used in a number of systematic microwave experiments [6,12], which in turn have been inspired by measurements of conductance and wave function scarring in source-drain biased open quantum dots with very A nominally symmetric hard-wall 2D cavity of height 21 cm and width 22 cm used in the calculations. The shaded rectangle is the region used to sample data for the statistical analysis.…”

“…[7,8] has been applied to a "twolead" planar [two-dimensional (2D)] quantum dot in a gated Al x Ga (1−x) As/GaAs heterostructure [11]. Particle densities and probability current flows for a selected set of low-energy states were compared with analog measurements for an equally shaped microwave resonator [12]. The resemblance between the two cases is noteworthy for the typical resonant states selected in that study.…”

Electrical Resonance Circuits as Analogs to Quantum Mechanical Billiards

“…This is the same billiard used in the microwave studies in Refs. [3][4][5][6],which originally was chosen to study wave function scarring al. [12], whereas Bengtsson et al [13] have focused on wave function statistics and how symmetry may be probed by external AC voltages.…”

“…For these reasons planar microwave cavities have been studied experimentally, for example, as in Refs. [3][4][5][6][7]. Figure 1 shows experimental results from Ref.…”

The distribution of extremal points of Gaussian scalar fields

“…The distribution of the nodal points keeps information about the degree of (orientational) order within the system, and about the topology of the 'substrate'. Well known examples are defects in liquid crystal films, vortices in thin superconductors and superfluid films (for an overview, see [1]), or chaotic wave functions in quantum mechanics [2], microwave billiards [3,4], and optical speckle pattern [5].…”