We investigate the nonreciprocal diodelike behavior of a dimer with an asymmetric on-site potential and a saturable nonlinearity. The dimer is coupled to linear side chains. The spectra of transmission and the rectifying factor are analytically obtained using a backward iteration of the set of discrete nonlinear Schrödinger equations used to model the wave propagation through the nonlinear dimer. We show that the windows of bistable behavior leading to a pronounced nonreciprocal diodelike transmission become wider and displaced to higher input field intensities as the saturation coefficient increases. Further, saturation of the nonlinear response has opposite impacts on the rectifying action over short- and long-wavelength input signals within the second bistability window. In the first window, the rectifying action is not compromised by the saturation, thus showing that a weak contribution of high-order susceptibilities to the nonlinear response can improve the efficiency of the nonreciprocal transmission. The rectifying action of a dimer with an asymmetric nonlinearity is also discussed.

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In this paper, we study the dynamics of a one-electron in a one-dimensional (1d) alloy with a correlated Ornstein-Uhlenbeck (OU) disorder distribution. The model considered here corresponds to an alloy with three types of atoms where the position of each atom is obtained using a stochastic rule based on the OU process. We analyze in detail the e®ect of this correlated disorder in the optical absorption spectrum and the level spacing statistics near the band center. Our results reveal a new collection of optical absorption peaks. We explain in details the appearance of each peak. Our calculations about the level spacing's distribution reveals a Poisson distribution thus contradicting previous statements about the existence of extended states in ternary electronic models with correlated disorder distribution.

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ nν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

We introduce a model system composed of two input discrete chains nonlinearly coupled to a single output chain which mimics the geometry of Y-shaped carbon nanotubes, photonic crystal wave guides, and DNA junctions. We explore the capability of the proposed system to perform logic gate operations based on the transmission of phase-shifted harmonic incoming waves. Within a tight-binding approach, we determine the exact transmission spectrum which exhibits a nonlinear induced bistability. Using a digitalization scheme of the output signal based on amplitude modulation, we show that AND, OR, and XOR logic operations can be achieved. Nonlinearity strongly favors the realization of logic operations in the regime of large wavelengths, while phase shifting is required for the OR logic gate to be realizable. A detailed analysis of the contrast ratio shows that optimal operation of the AND and OR logic gates takes place when the nonlinear response is the predominant physical property distinguishing the coupling and regular sites. These results point towards the possibility of Y-branched junctions to perform logic operations based on the transmission of traveling waves.