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

Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers

We consider a ${\rm A}_m{\rm B}_n$ diblock copolymer, whose links are capable of forming local reversible bonds with each other. We assume that the resulting structure of the bonds is RNA--like, i.e. topologically isomorphic to a tree. We show that, depending on the relative strengths of A--A, A--B and B--B contacts, such a polymer can be in one of two different states. Namely, if a self--association is preferable (i.e., A--A and B--B bonds are comparatively stronger than A--B contacts) then the polymer forms a typical randomly branched cloverleaf structure. On the contrary, if alternating association is preferable (i.e. A--B bonds are stronger than A--A and B--B contacts) then the polymer tends to form a generally linear necklace structure (with, probably, some rear side branches and loops, which do not influence the overall characteristics of the chain). The transition between cloverleaf and necklace states is studied in details and it is shown that it is a 2nd order phase transition.Comment: 17 pages, 9 figure

Statistics of layered zigzags: a two-dimensional generalization of TASEP

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.Comment: 5 pages, 4 figure

Vacuum Cherenkov radiation

Within the classical Maxwell-Chern-Simons limit of the Standard-Model Extension (SME), the emission of light by uniformly moving charges is studied confirming the possibility of a Cherenkov-type effect. In this context, the exact radiation rate for charged magnetic point dipoles is determined and found in agreement with a phase-space estimate under certain assumptions.Comment: 4 pages, REVTeX

Discrete surface solitons in semi-infinite binary waveguide arrays

We analyze discrete surface modes in semi-infinite binary waveguide arrays, which can support simultaneously two types of discrete solitons. We demonstrate that the analysis of linear surface states in such arrays provides important information about the existence of nonlinear surface modes and their properties. We find numerically the families of both discrete surface solitons and nonlinear Tamm (gap) states and study their stability properties.Comment: 3 pages, 4 figures, submitted to Opt. Let

Electronic structure of d-wave superconducting quantum wires

We present analytical and numerical results for the electronic spectra of wires of a d-wave superconductor on a square lattice. The spectra of Andreev and other quasiparticle states, as well as the spatial and particle-hole structures of their wave functions, depend on interference effects caused by the presence of the surfaces and are qualitatively different for half-filled wires with even or odd number of chains. For half-filled wires with an odd number of chains N at (110) orientation, spectra consist of N doubly degenerate branches. By contrast, for even N wires, these levels are split, and all quasiparticle states, even the ones lying above the maximal gap, have the characteristic properties of Andreev bound states. These Andreev states above the gap can be interpreted as a consequence of an infinite sequence of Andreev reflections experienced by quasiparticles along their trajectories bounded by the surfaces of the wire. Our microscopic results for the local density of states display atomic-scale Friedel oscillations due to the presence of the surfaces, which should be observable by scanning tunneling microscopy. For narrow wires the self-consistent treatment of the order parameter is found to play a crucial role. In particular, we find that for small wire widths the finite geometry may drive strong fluctuations or even stablilize exotic quasi-1D pair states with spin triplet character.Comment: 21 pages, 20 figures. Slightly modified version as published in PR

Observation of Surface-Avoiding Waves: A New Class of Extended States in Periodic Media

Coherent time-domain optical experiments on GaAs-AlAs superlattices reveal the exis-tence of an unusually long-lived acoustic mode at ~ 0.6 THz, which couples weakly to the environment by evading the sample boundaries. Classical as well as quantum states that steer clear of surfaces are generally shown to occur in the spectrum of periodic struc-tures, for most boundary conditions. These surface-avoiding waves are associated with frequencies outside forbidden gaps and wavevectors in the vicinity of the center and edge of the Brillouin zone. Possible consequences for surface science and resonant cavity ap-plications are discussed.Comment: 16 pages, 3 figure

The quantum vacuum at the foundations of classical electrodynamics

In the classical theory of electromagnetism, the permittivity and the permeability of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of the permittivity and the permeability, and for the volume of a virtual pair. Such interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak field limit.Comment: Accepted in Applied Physics B: Special Issue for the 50 years of the laser. Comments are welcome