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

Measuring the sequence-affinity landscape of antibodies with massively parallel titration curves

Despite the central role that antibodies play in the adaptive immune system and in biotechnology, much remains unknown about the quantitative relationship between an antibody's amino acid sequence and its antigen binding affinity. Here we describe a new experimental approach, called Tite-Seq, that is capable of measuring binding titration curves and corresponding affinities for thousands of variant antibodies in parallel. The measurement of titration curves eliminates the confounding effects of antibody expression and stability that arise in standard deep mutational scanning assays. We demonstrate Tite-Seq on the CDR1H and CDR3H regions of a well-studied scFv antibody. Our data shed light on the structural basis for antigen binding affinity and suggests a role for secondary CDR loops in establishing antibody stability. Tite-Seq fills a large gap in the ability to measure critical aspects of the adaptive immune system, and can be readily used for studying sequence-affinity landscapes in other protein systems

The Structure of Allelic Diversity in the Presence of Purifying Selection

In the absence of selection, the structure of equilibrium allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped shape our expectations of empirical patterns of molecular variation. Along with coalescent theory, it provides statistical techniques for rejecting the null model of neutrality. However, we still do not fully understand the statistics of the allelic diversity expected in the presence of natural selection. Earlier work has described the effects of strongly deleterious mutations linked to many neutral sites, and allelic variation in models where offspring fitness is unrelated to parental fitness, but it has proven difficult to understand allelic diversity in the presence of purifying selection at many linked sites. Here, we study the population genetics of infinitely many perfectly linked sites, some neutral and some deleterious. Our approach is based on studying the lineage structure within each class of individuals of similar fitness in the deleterious mutation-selection balance. Consistent with previous observations, we find that for moderate and weak selection pressures, the patterns of allelic diversity cannot be described by a neutral model for any choice of the effective population site. We compute precisely how purifying selection at many linked sites distorts the patterns of allelic diversity, by developing expressions for the likelihood of any configuration of allelic types in a sample analogous to the Ewens sampling formula.Organismic and Evolutionary Biolog

The Structure of Genealogies in the Presence of Purifying Selection: a "Fitness-Class Coalescent"

Compared to a neutral model, purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation. Although these distortions may be common in nature, our understanding of how we expect purifying selection to affect patterns of molecular variation remains incomplete. Genealogical approaches such as coalescent theory have proven difficult to generalize to situations involving selection at many linked sites, unless selection pressures are extremely strong. Here, we introduce an effective coalescent theory (a "fitness-class coalescent") to describe the structure of genealogies in the presence of purifying selection at many linked sites. We use this effective theory to calculate several simple statistics describing the expected patterns of variation in sequence data, both at the sites under selection and at linked neutral sites. Our analysis combines a description of the allele frequency spectrum in the presence of purifying selection with the structured coalescent approach of Kaplan et al. (1988), to trace the ancestry of individuals through the distribution of fitnesses within the population. We also derive our results using a more direct extension of the structured coalescent approach of Hudson and Kaplan (1994). We find that purifying selection leads to patterns of genetic variation that are related but not identical to a neutrally evolving population in which population size has varied in a specific way in the past.Organismic and Evolutionary Biolog

Modeling transport through single-molecule junctions

Non-equilibrium Green's functions (NEGF) formalism combined with extended Huckel (EHT) and charging model are used to study electrical conduction through single-molecule junctions. Analyzed molecular complex is composed of asymmetric 1,4-Bis((2'-para-mercaptophenyl)-ethinyl)-2-acetyl-amino-5-nitro-benzene molecule symmetrically coupled to two gold electrodes [Reichert et al., Phys. Rev. Lett. Vol.88 (2002), pp. 176804]. Owing to this model, the accurate values of the current flowing through such junction can be obtained by utilizing basic fundamentals and coherently deriving model parameters. Furthermore, the influence of the charging effect on the transport characteristics is emphasized. In particular, charging-induced reduction of conductance gap, charging-induced rectification effect and charging-generated negative value of the second derivative of the current with respect to voltage are observed and examined for molecular complex.Comment: 8 pages, 3 figure