Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version (PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902 (2001) (E

Phase transitions in a network with range dependent connection probability

We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit small world behaviour for $\delta < 2$ above which its behaviour is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at $\delta = 1$. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicate that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behaviour of a single quantity, the average bond length. The phase transitions in all dimensions are non-trivial in nature.Comment: 4 pages, revtex4, submitted to Physical Review

Alternative Technique for "Complex" Spectra Analysis

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes

Scaling in DNA unzipping models: denaturated loops and end-segments as branches of a block copolymer network

For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end-segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first order thermal denaturation in both cases. Results for end-segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, are explained in terms of a refined scaling picture in which a precise distinction is made between network branches representing single stranded and effective double stranded segments.Comment: 8 pages, 8 figure

Atomic-scale perspective on the origin of attractive step interactions on Si(113)

Recent experiments have shown that steps on Si(113) surfaces self-organize into bunches due to a competition between long-range repulsive and short-range attractive interactions. Using empirical and tight-binding interatomic potentials, we investigate the physical origin of the short-range attraction, and report the formation and interaction energies of steps. We find that the short-range attraction between steps is due to the annihilation of force monopoles at their edges as they combine to form bunches. Our results for the strengths of the attractive interactions are consistent with the values determined from experimental studies on kinetics of faceting.Comment: 4 pages, 3 figures, to appear in Phys. Rev B, Rapid Communication

Unzipping Dynamics of Long DNAs

The two strands of the DNA double helix can be `unzipped' by application of 15 pN force. We analyze the dynamics of unzipping and rezipping, for the case where the molecule ends are separated and re-approached at constant velocity. For unzipping of 50 kilobase DNAs at less than about 1000 bases per second, thermal equilibrium-based theory applies. However, for higher unzipping velocities, rotational viscous drag creates a buildup of elastic torque to levels above kBT in the dsDNA region, causing the unzipping force to be well above or well below the equilibrium unzipping force during respectively unzipping and rezipping, in accord with recent experimental results of Thomen et al. [Phys. Rev. Lett. 88, 248102 (2002)]. Our analysis includes the effect of sequence on unzipping and rezipping, and the transient delay in buildup of the unzipping force due to the approach to the steady state.Comment: 15 pages Revtex file including 9 figure

A pseudo-spectral method for the Kardar-Parisi-Zhang equation

We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the non-linear term. The method is tested in (1+1)- and (2+1)- dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on Restricted Solid-on-Solid simulations. In particular it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies which are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.Comment: 12 pages, 13 .eps figures, revetx4. A few equations have been corrected. Erratum sent to Phys. Rev.

Soliton Lattices in the Incommensurate Spin-Peierls Phase: Local Distortions and Magnetizations

It is shown that nonadiabatic fluctuations of the soliton lattice in the spin-Peierls system CuGeO_3 lead to an important reduction of the NMR line widths. These fluctuations are the zero-point motion of the massless phasonic excitations. Furthermore, we show that the discrepancy of X-ray and NMR soliton widths can be understood as the difference between a distortive and a magnetic width. Their ratio is controlled by the frustration of the spin system. By this work, theoretical and experimental results can be reconciled in two important points.Comment: 9 pages, 5 figures included, Revtex submitted to Physical Review

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Nearby quasar remnants and ultra-high energy cosmic rays

As recently suggested, nearby quasar remnants are plausible sites of black-hole based compact dynamos that could be capable of accelerating ultra-high energy cosmic rays (UHECRs). In such a model, UHECRs would originate at the nuclei of nearby dead quasars, those in which the putative underlying supermassive black holes are suitably spun-up. Based on galactic optical luminosity, morphological type, and redshift, we have compiled a small sample of nearby objects selected to be highly luminous, bulge-dominated galaxies, likely quasar remnants. The sky coordinates of these galaxies were then correlated with the arrival directions of cosmic rays detected at energies $> 40$ EeV. An apparently significant correlation appears in our data. This correlation appears at closer angular scales than those expected when taking into account the deflection caused by typically assumed IGM or galactic magnetic fields over a charged particle trajectory. Possible scenarios producing this effect are discussed, as is the astrophysics of the quasar remnant candidates. We suggest that quasar remnants be also taken into account in the forthcoming detailed search for correlations using data from the Auger Observatory.Comment: 2 figures, 4 tables, 11 pages. Final version to appear in Physical Review