arXiv subjects

Oleg Tymoshchuk

Publications and source records attributed to Oleg Tymoshchuk.

4 recordsLinked to original sources

arXiv2009

Investigation of nodal domains in a chaotic three-dimensional microwave rough billiard with the translational symmetry

We show that using the concept of the two-dimensional level number N_{|} one can experimentally study of the nodal domains in a three-dimensional (3D) microwave chaotic rough billiard with the translational symmetry. Nodal domains are regions where a wave function has a definite sign. We found the dependence of the number of nodal domains aleph_{N_{|}} lying on the cross-sectional planes of the cavity on the two-dimensional level number N_{|}. We demonstrate that in the limit N_{|} -> infinity the least squares fit of the experimental data reveals the asymptotic ratio aleph_{N_{|}}/N_{|} = 0.059 +- 0.029 that is close to the theoretical prediction aleph_{N_{|}}/N_{|} = 0.062. This result is in good agreement with the predictions of percolation theory.

nlin.CD↗

arXiv2009

Experimental investigation of electric field distributions in a chaotic 3D microwave rough billiard

We present the first experimental study of the electric field distributions E_N of a three-dimensional (3D) microwave chaotic rough billiard with the translational symmetry. The translational symmetry means that the cross-section of the billiard is invariant under translation along z direction. The 3D electric field distributions were measured up to the level number N = 489. In this way the experimental spatial correlation functions C_{N,p}(x,s) ~ < E_{N,p}(x+1/2*s) E_{N,p}^(*)(x - 1/2*s)> were found and compared with the theoretical ones. The experimental results for higher two-dimensional level number N_{|} appeared to be in good agreement with the theoretical predictions.

nlin.CD↗

arXiv2009

Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

We use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by T-joints to make an experimental study of Wigner's reaction K matrix for irregular graphs in the presence of absorption. From measurements of the scattering matrix S for each realization of the microwave network we obtain distributions of the imaginary and real parts of K. Our experimental results are in good agreement with theoretical predictions.

nlin.CD↗

arXiv2009

Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard

We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Shnirelman ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. For this aim the wave functions Psi_N of the billiard were measured up to the level number N=415. We show that in the regime of Shnirelman ergodicity (N>208) wave functions of the chaotic half-circular microwave ray-splitting rough billiard are extended over the whole energy surface and the amplitude distributions are Gaussian. For such ergodic wave functions the dependence of the number of nodal domains aleph_N on the level number N was found. We show that in the limit N->infty the least squares fit of the experimental data yields aleph_N/N = 0.063 +- 0.023 that is close to the theoretical prediction aleph_N/N = 0.062. We demonstrate that for higher level numbers N = 215-415 the variance of the mean number of nodal domains sigma^2_N/ N is scattered around the theoretical limit sigma^2_N /N = 0.05. We also found that the distribution of the areas s of nodal domains has power behavior n_s ~ s^{-tau}, where the scaling exponent is equal to tau = 2.14 +- 0.12. This result is in a good agreement with the prediction of percolation theory.

nlin.CD↗