Measurement of Long-Range Wave-Function Correlations in an Open Microwave Billiard

We investigate the statistical properties of wave functions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wave functions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wave function is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.

Figure 1

Left panel: Grey scale plot of measured intensity $|\psi {|}^2$ at $\nu =12.015\mathrm{G}\mathrm{H}\mathrm{z}$. Black corresponds to maximum intensity. Right panel: Corresponding current density. Arrow lengths indicate the magnitude of the Poynting vector.

Figure 2

Intensity distribution for the wave function at $\nu =12.015\mathrm{G}\mathrm{H}\mathrm{z}$. Theoretical values are plotted with a solid line.

Figure 3

Phase rigidity distribution $P(|\rho {|}^2)$ for different channel numbers $N$. Solid curves indicate the theory of Ref. 12.

Figure 4

Connected correlator $⟨I(\mathbf{r}{)}^{2}I({\mathbf{r}}^{\prime }{)}^2{⟩}_c$ of squared intensity versus $k|\mathbf{r}-{\mathbf{r}}^{\prime }|$ for different channel numbers $N$.

Figure 5

As Fig. 4, but for $⟨I(\mathbf{r}{)}^{2}J({\mathbf{r}}^{\prime }{)}^2{⟩}_c$.

Figure 6

As Fig. 4, but for $⟨J(\mathbf{r}{)}^{2}J({\mathbf{r}}^{\prime }{)}^2{⟩}_c$.