Lamplighter model of a random copolymer adsorption on a line

We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.Comment: 8 pages, 5 figure

Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid

In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the 1D electron gas and 2D Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozieres-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the 1D case but finding no changes in the DOS of the 2D Hall fluid with short-range interaction. We also provide, for the first time, an exact solution of the Nozieres-De Dominicis equation for the 2D electron gas in the lowest Landau level.Comment: 6 pages, Revte

Polarons in suspended carbon nanotubes

We prove theoretically the possibility of electric-field controlled polaron formation involving flexural (bending) modes in suspended carbon nanotubes. Upon increasing the field, the ground state of the system with a single extra electron undergoes a first order phase transition between an extended state and a localized polaron state. For a common experimental setup, the threshold electric field is only of order $\simeq 10^{-2}$ V/$\mu$m

Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment

Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long range character, resulting in $\log^2$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order, and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function, while all other quantities renormalize only logarithmically. We solve the RG flow equation for the Green function with logarithmic accuracy, and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge invariant quantities, such as the compressibility, remain finite to $\log^2$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the non-interacting value.Comment: 12 pages, 3 figure

Simulation of Atomic Structure Near Nanovoids in BCC Iron

Generally, displacement fields near voids are determined by the equations of elasticity theory. Such a description has its disadvantages as it does not take into account the discrete atomic structure of materials. In this work, we use a new variant of Molecular Static method for investigation of the atomic structure near nanovoids. In our model an iterative procedure is employed, in which the atomic structure in the void vicinity and the parameter determining the displacement of atoms embedded into an elastic continuum are obtained in a self-consistent manner. Results show that the displacements are significantly different for varies crystallographic directions. Keywords: voids; iron; simulation; atomic structure; vacancie