Search

The Poisson equation is used to calculate the drift velocity in the two-dimensional diffusion couple. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multicomponent mixture at non-equilibrium. As an example the arbitrary binary system is considered. It is shown that (1) the two dimensional calculations should be applied with the stochastization method and (2) the drift term in mass conservation law does not affect the calculations. [ABSTRACT FROM AUTHOR]

Within the BCS theory of superconductivity we calculate the superconducting gap at a zero-temperature for metallic hydrogen–graphene system in order to estimate the superconducting critical temperature of quasi-two-dimensional highly oriented pyrolytic graphite. The obtained results are given as a function of the hydrogen-induced density of carriers n and their effective mass m ⋆. The obtained gap shows a Maxwell-like distribution with a maximum of ∼60 K at n∼3×1014 cm−2 and m ⋆/ m=1. The theoretical results are discussed taking into account recent experimental evidence for granular superconductivity in graphite. [ABSTRACT FROM AUTHOR]

We show the insulating region of the metal-insulator transition phenomena in disordered two-dimensional electron systems contains new information about the quantum critical dynamics at low T because the insulating region and the quantum critical region are two aspects of the localized phase. [ABSTRACT FROM AUTHOR]

• 2D split-ring resonator array with resonant frequency disorder. • Localized modes and magnetic transport for uncorrelated and correlated disorder in 2D. • Correlated disorder can create sub-diffusive propagation. We study the effect of a resonant frequency disorder on the eigenstates and the transport of magnetic energy in a two-dimensional (square) array of split-ring resonators (SRRs). In the absence of disorder, we find the dispersion relation of magneto-inductive waves and the mean square displacement (MSD) in closed form, showing that at long times the MSD is ballistic. When disorder is present, we consider two types: the usual Anderson distribution (uncorrelated monomers) and 2 × 2 units assigned at random to lattice sites (correlated tetramers). This is a direct extension to two dimensions of the one-dimensional random dimer model (RDM). For the uncorrelated case, we see saturation of the MSD for all disorder widths, while for the correlated case we find a disorder window, inside which the MSD does not saturate at long times, with an asymptotic sub-diffusive behavior M S D ∼ t 0.26. Outside this disorder window, the MSD shows the same kind of saturation as in the monomer case. We conjecture that the sub-diffusive behavior is a remanent of a weak resonant transmission of a 2D plane wave across a tetramer unit. [ABSTRACT FROM AUTHOR]

• Some two dimensional Schrödinger equations have solutions for which the amplitudes and phases can be interchanged. • This only occurs when the Bohm potential vanishes, and for negative potentials. • These solutions represent particles with equal energy but different momenta, evolving in the same potential. • Exact solutions for physical systems, as repulsive harmonic oscillator or hydrogen atom, are found. • This system has a correspondence with optics, which implies that dual solutions can be studied in analogue optical systems. It is shown that the Schrödinger equation for a large family of pairs of two–dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Böhm potential. These solutions can be extended to three–dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two–dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two–dimensional dual wavefunction solutions with an optical (analogue) system. [ABSTRACT FROM AUTHOR]