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We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. Poisson photocount distribution of the incident light widens and gains additional asymmetry upon transmission through a suspension of small dielectric spheres. The effect is only appreciable when the average number <n> of photocounts becomes comparable or larger than the effective dimensionless conductance g of the sample.
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We study the dependence of the glassy properties of strongly localized indium-oxide films on the sample lateral dimensions. Characteristic mesoscopic effects such as reproducible conductance fluctuations (CF) are readily observable in gated structures for sample size smaller than 100 microns measured at 4K, and the relative amplitude of the CF decreases with the sample volume as does the flicker noise. By contrast, down to sample size of few microns, the non-equilibrium features that are attributed to the electron-glass are indistinguishable from those observed in macroscopic samples, and in particular, the relaxation dynamics is independent of sample size down to 2 microns. In addition, The usual features that characterize the electron-glass including slow-relaxation, memory effects, and full-aging behavior are all observed in the `mesoscopic regime, and they appear to be independent of the conductance fluctuations.
We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.
Quasiparticle states in Dirac systems with complex impurity potentials are investigated. It is shown that an impurity site with loss leads to a nontrivial distribution of the local density of states (LDOS). While the real part of defect potential induces a well-pronounced peak in the density of states (DOS), the DOS is either weakly enhanced at small frequencies or even forms a peak at the zero frequency for a lattice in the case of non-Hermitian impurity. As for the spatial distribution of the LDOS, it is enhanced in the vicinity of impurity but shows a dip at a defect itself when the potential is sufficiently strong. The results for a two-dimensional hexagonal lattice demonstrate the characteristic trigonal-shaped profile for the LDOS. The latter acquires a double-trigonal pattern in the case of two defects placed at neighboring sites. The effects of non-Hermitian impurities could be tested both in photonic lattices and certain condensed matter setups.
We introduce a class of critical states which are embedded in the continuum (CSC) of one-dimensional optical waveguide array with one non-Hermitian defect. These states are at the verge of being fractal and have real propagation constant. They emerge at a phase transition which is driven by the imaginary refractive index of the defect waveguide and it is accompanied by a mode segregation which reveals analogies with the Dicke super -radiance. Below this point the states are extended while above they evolve to exponentially localized modes. An addition of a background gain or loss can turn these localized states to bound states in the continuum.
We study the statistical properties of the complex generalization of Wigner time delay $tau_text{W}$ for sub-unitary wave chaotic scattering systems. We first demonstrate theoretically that the mean value of the $text{Re}[tau_text{W}]$ distribution function for a system with uniform absorption strength $eta$ is equal to the fraction of scattering matrix poles with imaginary parts exceeding $eta$. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels, and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave chaotic scattering system in the short-wavelength limit.
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