The anomalous effect of surface diffusion on the nuclear magnetic resonance signal in restricted geometry.

Anisotropy of diffusion properties in a specimen plays a key role in numerous applications of nuclear magnetic resonance (NMR) imaging, like non-invasive tracking of fibers in the central nervous system. We suggest that contrasting fiber structures with certain diameters could be improved if second-order effects are taken into account. We introduce a procedure consisting of two standard diffusion NMR experiments differing in their gradient pulse characteristics. These two echo signals will be called the background and principal signals. We show that the difference obtained by subtracting one echo signal from the other has either typical or anomalous properties. In the typical case, as the duration of the gradient pulse in the second experiment is set to smaller and smaller values, the difference from the background echo signal tends toward its maximum. In contrast, in the anomalous case the difference between the background and the principal signals has a maximum at a certain nonzero duration of the pulse in the second experiment. This critical duration is determined by different characteristics, including the diameters of fibers. For this anomalous effect to take place the fast surface diffusion channel coupled to the surrounding media is required. The diffusion of magnetic molecules along the surface of restricted media and the coupling of the surface and the bulk translational motions can strongly modify the echo attenuation NMR signal. The origin of this strong anomalous effect is the change of the symmetry of the lowest diffusion eigenmode of the system. We illustrate the effect of surface diffusion for a cylindrically symmetric system and describe the experimental conditions under which the anomalous behavior of the echo signals can be observed.

Localized modes in one-dimensional nonlinear periodic photonic structures.

We study the generation of localized second-harmonic modes in a one-dimensional photonic crystal with a defect in the form of a phase slip. Due to the presence of the defect the photonic crystal has localized in-gap modes. We consider the case when the fundamental mode is localized in the first bandgap and because of its nonlinear properties it generates a localized second-harmonic mode. As a function of the parameters of the photonic crystal and the defect the intensity of the second-harmonic mode has sharp maxima, which correspond to the resonance condition, i.e. the frequency of the second-harmonic mode is equal to the frequency of the localized mode in the second bandgap. We find the conditions when such resonance can be achieved. We also determine the optimal parameters of the photonic crystal at which the generation of the second-harmonic mode becomes less sensitive to violation of the resonance condition.

Incomplete photonic band gap as inferred from the speckle pattern of scattered light waves.

Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band gap represents a sensitive tool for determination of the stop-band width. We establish the quantitative relation between this width and the angular anisotropy of the intensity correlation function.

Anomalously localized states in the Anderson model.

It is demonstrated that anomalously localized states (ALS) in the Anderson model, being lattice specific, are not related to any of the continuous theories. We identify the spatial structure of ALS on a lattice and calculate their likelihood. Analytical results explain peculiarities in previous numerical simulations.

Optical probing of a fractionally charged quasihole in an incompressible liquid.

In photoluminescence spectroscopy of a low-mobility two-dimensional electron gas subjected to a quantizing magnetic field, we observe an anomaly around nu=1 / 3 at a very low temperature (0.1 K) and an intermediate electron density (0.9 x 10(11) cm(-2)). The anomaly is explained as due to perturbation of the incompressible liquid at the Laughlin state due to close proximity of a localized charged exciton which creates a fractionally charged quasihole in the liquid. The anomaly of approximately 2 meV can be destroyed by applying a small thermal energy of approximately 0.2 meV that is enough to close the quasihole energy gap.

Strongly localized mode at the intersection of the phase slips in a photonic crystal without band gap.

A two-dimensional photonic crystal with a rectangular symmetry and low contrast (<1) of the dielectric constant is considered. We demonstrate that, despite the absence of a band gap, strong localization of a photon can be achieved for certain "magic" geometries of a unit cell by introducing two pi/2 phase slips along the major axes. The long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry-a square lattice of cylinders of a radius, r. We find the magic radius r(c) of a cylinder to be 43.10% of the lattice constant. For this value of r, the quality factor of the bound mode exceeds 10(6). A small ( approximately 1%) deviation of r from r(c) results in a drastic damping of the bound mode.

Crossover between universality classes in the statistics of rare events in disordered conductors.

The crossover from orthogonal to the unitary universality classes in the distribution of the anomalously localized states (ALS) in two-dimensional disordered conductors is traced as a function of magnetic field. We demonstrate that the microscopic origin of the crossover is the change in the symmetry of the underlying disorder configurations that are responsible for ALS. These disorder configurations are of weak magnitude (compared to the Fermi energy) and of small size (compared to the mean free path). We find their shape explicitly by means of the direct optimal fluctuation method.

Zero-field satellites of a zero-bias anomaly.

Spin-orbit (SO) splitting, +/-omega(SO), of the electron Fermi surface in two-dimensional systems manifests itself in the interaction-induced corrections to the tunneling density of states, nu(epsilon). Namely, in the case of a smooth disorder, it gives rise to the satellites of a zero-bias anomaly at energies epsilon = +/-2 omega(SO). Zeeman splitting, +/-omega(Z), in a weak parallel magnetic field causes a narrow plateau of a width delta epsilon = 2 omega(Z) at the top of each sharp satellite peak. As omega(Z) exceeds omega(SO), the SO satellites cross over to the conventional narrow maxima at epsilon = +/-2 omega(Z) with SO-induced plateaus delta epsilon = 2 omega(SO) at the tops.

Random resonators and prelocalized modes in disordered dielectric films.

We calculate the areal density of disorder-induced resonators with a high quality factor, Q>>1, in a film with fluctuating refraction index. We demonstrate that, for a given kl>1, where k is the light wave vector and l is the transport mean-free path, when on average the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of most probable resonators as functions of Q and kl are found.

Half-polarized quantum hall states.

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.