Concentric layered Hermite scatterers

The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering $k^2$ power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.     

Macroscopic behaviour of a charged Boltzmann gas

We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzmann equation with thermalization on uniformly distributed scatterers. It is shown that if one scales the time t, the reciprocal space coordinate k and the Debye length l as λ²t, (1/λ)k, λl, respectively, in the λ → ∞ limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation.     

Quantum transport in lattices of coupled electronic billiards

A new system with dynamic chaos—2D lattice of single Sinai billiards coupled through quantum dots—is studied experimentally. Localization in such a system was found to be substantially suppressed, because the characteristic size of the billiard for g≤1 (g is conductance measured in e ₂/h units) is the localization length rather than the de Broglie wavelength of an electron, as in the usual 2D electron system. Lattice ballistic effects (commensurate peaks in the magnetoresistance) for g?1, as well as extremely large magnetoresistance caused by the interference in chaotic electron trajectories, were found. Thus, this system is shown to be characterized by simultaneous existence of effects that are inherent in order (commensurate peaks of magnetoresistance), disorder (percolation charge transport), and chaos (weak localization in chaotic electron trajectories).     

Enhancement of localization in one-dimensional random potentials with long-range correlations

We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers.     

Stochastic frequency-domain tissue characterization: application to human spleens ‘in vivo’

Ultrasonic waveforms backscattered from normal and pathologic human spleens were recorded in vivo using a high-speed digital data acquisition system. A frequency-domain analysis was performed for 50 digitized waveforms from each spleen, in which auto-correlations of frequency spectra were employed to measure the mean spacing among adjacent tissue scatterers. Mean scatterer spacing for normal spleens averaged 1.10 ± 0.14 mm, whereas abnormal, diffusely enlarged spleens had mean scatterer spacings averaging 1.52 ± 0.14 mm. The results of these measurements are in accord with those expected from splenic histology. The techniques described may be valuable in ultrasonic diagnosis of the spleen and other organs.     

Atomic structure effects of a target on the polarization properties of high harmonics in the region of the cooper minimum

Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111, 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111, 240402 (2013)] is unnecessary.     

Growth,structure and physical properties of gadolinium doped Sr2IrO4 single crystal

A series of Gd-doped Sr₂IrO₄ single crystals were grown using a flux method. Analysis of the temperature-dependent resistance of these crystals reveals that these samples show two-dimensional weak localization at 150 to 300 K, while three-dimensional variable range hopping (VRH) behavior is observed at temperatures lower than 150 K. Two localization lengths are observed in the VRH behavior, with a transition temperature of around 88 K. Correspondingly, temperature-dependent magnetization observations along the ab-plane reveal magnetic anomalies at both 150 and 85 K. This work demonstrates the correlation between the electrical and magnetic properties of 5d transition-metal compounds.     

Projection Presaturation. III. Accurate Selective Excitation or Presaturation of the Regions of Tailored Shape in the Presence of Short-T1 Species

A new method is described which further increases the accuracy of localization by projection presaturation (PP), a technique for multidimensional spatial localization of contoured regions of interest (ROIs), whose shape, size, position, and number can be chosen arbitrarily (J. Magn. Reson.90, 313, 1990). By applying a nonselective radiofrequency inversion pulse after the PP saturation cycle and nulling the residual longitudinal magnetization of the region outside the ROI, the outer-volume signal is suppressed to the "noise" level, thus improving the accuracy of the basic PP localization, even when saturating a large exterior volume of short-T₁ species. The ability of the method to perform spatial and spectral localization simultaneously is also described. Alternatively, the single-shot methods for selective saturation (instead of selective excitation) of single or multiple contoured regions at arbitrary positions in an extended volume are presented. In particular, the results of selective excitation and saturation of a region of conformal geometric shape in two and three dimensions in a phantom as well as in vivo (healthy volunteers) are presented to demonstrate the efficacy of the method. Applications of these methods include flow- and motion-artifact suppression in body MRI, accurate conformal localization for in vivo spectroscopy in the presence of chemical shift, outer-volume suppression for resolution or speed enhancement in ultrafast imaging (Magn. Reson. Med.13, 77, 1990; J. Phys. C10, L55, 1977), and spin tagging by selective excitation/saturation of flowing spins for flow studies and angiography.     

Field Confinement Energy at a Nonlinear Interface between Nonlinear Defocusing Media

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS₃ on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T₀ ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T₀. The negative magnetoresistance (at B ∥ c) below T₀ is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.     

Weak localization in monolayer and bilayer graphene

We describe the weak localization correction to conductivity in ultra-thin graphene films, taking into account disorder scattering and the influence of trigonal warping of the Fermi surface. A possible manifestation of the chiral nature of electrons in the localization properties is hampered by trigonal warping, resulting in a suppression of the weak anti-localization effect in monolayer graphene and of weak localization in bilayer graphene. Intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore weak localization resulting in negative magnetoresistance in both materials.     

Low-temperature hopping conduction over the upper Hubbard band in p-GaAs/AlGaAs multilayered structures

The low-temperature 2D variable range hopping conduction over the states of the upper Hubbard band is investigated in detail for the first time in multilayered Be-doped p-type GaAs/AlGaAs structures with quantum wells of 15-nm width. This situation was realized by doping the layer in the well and a barrier layer close to the well for the upper Hubbard band (A ⁺ centers) in the equilibrium state filled with holes. The conduction was of the Mott hopping type in the entire temperature range (4?0.4 K). The positive and negative magnetoresistance branches as well as of non-Ohmic hopping conduction at low temperature are analyzed. The density of states and the localization radius, the scattering amplitude, and the number of scatterers in the upper Hubbard band are estimated. It is found that the interference pattern of phenomena associated with hopping conduction over the A ⁺ band is qualitatively similar to the corresponding pattern for an ordinary impurity band, but the tunnel scattering is relatively weak.     

Systematic Density Expansion of the Lyapunov Exponents for a Two-Dimensional Random Lorentz Gas

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders in the density of scatterers it is of the form A ₀ñln ñ+B ₀ñ, where A ₀ and B ₀ are known constants and ñ is the number density of scatterers expressed in dimensionless units. In this paper, we find that through order (ñ²), the positive Lyapunov exponent is of the form A ₀ñln ñ+B ₀ñ+A ₁ñ²ln ñ +B ₁ñ². Explicit numerical values of the new constants A ₁ and B ₁ are obtained by means of a systematic analysis. This takes into account, up to O(ñ²), the effects of all possible trajectories in two versions of the model; in one version overlapping scatterer configurations are allowed and in the other they are not.     

Three-dimensional interference effects in the mechanical action of weak biharmonic fields upon particles with the J=0 → J=1 quantum transition

Explicit expressions are derived for the rectified radiative forces (RRFs) related to the action of a weak interfering optical field of an arbitrary three-dimensional (3D) configuration upon resonance particles featuring the J=0 → J=1 quantum transition. It is shown that, in contrast to the case of a monochromatic field, there are simple 3D biharmonic field configurations for which the ratio of the vortex and potential RRF components can be controlled by adjusting frequencies and polarizations of the interfering light waves. This modification of the RRF structure gives rise to qualitatively different types of both vortex and potential light-induced particle motions that may lead to a 3D spatial localization (confinement) of these particles within the cells of an effective optical lattice with a period significantly greater than the light wavelength. In particular, the particles may perform a stable rotational motion along closed trajectories inside the elementary cells.     

Polarization-based range-gated imaging in birefringent medium:Effect of size parameter

We have investigated the effect of size parameter of the scatterer on the image quality obtained with polarization-based range-gated imaging in birefringent turbid medium. Both linearly and circularly polarized light were utilized for imaging.The simulated results indicate that the improvement of visibility is more pronounced using circularly polarized light for the birefringent medium composed of smaller-sized scatterers at lower values of optical thickness and the birefringent medium comprising larger-sized scatterers. In contrast, linearly polarized light provides better image quality for the birefringent medium composed of smaller-sized scatterers at larger values of optical thickness. The evolution of the polarization characteristics of backscattered light and target light under the conditions mentioned above was measured to account for these numerical results.     

Condensation of interacting bosons in a random potential

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval.     

Theoretical study on transport properties of a BN co-doped SiC nanotube

We investigate the electronic transport properties of silicon carbide nanotubes (SiCNT) in presence of both boron (B) and nitrogen (N) impurities. The results show that co-doping BN impurities suppresses the important negative differential resistance (NDR) property. NDR suppression is attributed to the introduction of new electronic states near the Fermi level followed by weak orbital localization. BN co-doping results in exponential current-voltage (I-V) characteristics which is in contrast to linear I-V characteristics for individual boron and nitrogen doped SiCNTs. HOMO has no contribution from B impurity, whereas, LUMO has contribution from N impurity at low and high bias.     

Theory of Anderson localization in weak magnetic fields

We derive self-consistency equations determining the transverse dynamical conductivity for the case of Wegner's local gauge invariant model in a weak magnetic field B. The solution in the critical regime connected with Anderson localization is given for dimensionalities d = 2, 3. In d = 2 the self-consistency equations generate a logarithmic singularity in second order in the coupling constant. This is shown to be in agreement with the loop expansion and yields localization for arbitrarily weak coupling. In d = 3 there is a metal-insulator transition. In its vicinity the self-consistency equations reduce to a two-parameter scaling law, which is consistent with the results of Khmelnitskii and Larkin.     

On Noether's theorem in quantum field theory

Extending the construction of local generators of symmetries in (S. Doplicher, Commun. Math. Phys.85 (1982), 73; S. Doplicher and R. Longo, Commun. Math. Phys.88 (1983), 399) to space-time and supersymmetries, we establish a weak form of Noether's theorem in quantum field theory. We also comment on the physical significance of the “split property,” underlying our analysis, and discuss some local aspects of superselection rules following from our results.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.