Back-reaction of perturbation wave packets on gray solitons

Within the Bogoliubov-de Gennes linearization theory of quantum or classical perturbations around a background solution to the one-dimensional nonlinear Schr\"odinger equation, we study the back-reaction of wave packet perturbations on a gray soliton background. From our recently published exact solutions, we determine that a wave packet effectively jumps ahead as it passes through a soliton, emerging with a wavelength-dependent forward translation in comparison to its motion in absence of the soliton. From this and from the full theory's exact momentum conservation, we deduce that post-Bogoliubov back-reaction must include a commensurate forward advance by the soliton itself. We quantify this effect with a simple theory, and confirm that it agrees with full numerical solution of the classical nonlinear Schr\"odinger equation. We briefly discuss the implications of this effect for quantum behavior of solitons in quasi-condensed dilute gases at finite temperature.Comment: 12 pages, 2 figure

Electron transport through multilevel quantum dot

Quantum transport properties through some multilevel quantum dots sandwiched between two metallic contacts are investigated by the use of Green's function technique. Here we do parametric calculations, based on the tight-binding model, to study the transport properties through such bridge systems. The electron transport properties are significantly influenced by (a) number of quantized energy levels in the dots, (b) dot-to-electrode coupling strength, (c) location of the equilibrium Fermi energy $E_F$ and (d) surface disorder. In the limit of weak-coupling, the conductance ($g$) shows sharp resonant peaks associated with the quantized energy levels in the dots, while, they get substantial broadening in the strong-coupling limit. The behavior of the electron transfer through these systems becomes much more clearly visible from our study of current-voltage ($I$-$V$) characteristics. In this context we also describe the noise power of current fluctuations ($S$) and determine the Fano factor ($F$) which provides an important information about the electron correlation among the charge carriers. Finally, we explore a novel transport phenomenon by studying the surface disorder effect in which the current amplitude increases with the increase of the surface disorder strength in the strong disorder regime, while, the amplitude decreases in the limit of weak disorder. Such an anomalous behavior is completely opposite to that of bulk disordered system where the current amplitude always decreases with the disorder strength. It is also observed that the current amplitude strongly depends on the system size which reveals the finite quantum size effect.Comment: 12 pages, 7 figure

A mesoscopic ring as a XNOR gate: An exact result

We describe XNOR gate response in a mesoscopic ring threaded by a magnetic flux $\phi$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the inputs of the XNOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strength, magnetic flux and gate voltages. Our theoretical study shows that, for a particular value of $\phi$ ($=\phi_0/2$) ($\phi_0=ch/e$, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the two inputs to the gate are the same, while if one but not both inputs are high (1), a low output current (0) results. It clearly exhibits the XNOR gate behavior and this aspect may be utilized in designing an electronic logic gate.Comment: 8 pages, 5 figure