Phase transition of one dimensional bosons with strong disorder

We study one dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott-glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.Comment: 4 pages 3 embedded eps figure

Phase transition in a non-conserving driven diffusive system

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes

Sequence heterogeneity and the dynamics of molecular motors

The effect of sequence heterogeneity on the dynamics of molecular motors is reviewed and analyzed using a set of recently introduced lattice models. First, we review results for the influence of heterogenous tracks such as a single-strand of DNA or RNA on the dynamics of the motors. We stress how the predicted behavior might be observed experimentally in anomalous drift and diffusion of motors over a wide range of parameters near the stall force and discuss the extreme limit of strongly biased motors with one-way hopping. We then consider the dynamics in an environment containing a variety of different fuels which supply chemical energy for the motor motion, either on a heterogeneous or on a periodic track. The results for motion along a periodic track are relevant to kinesin motors in a solution with a mixture of different nucleotide triphosphate fuel sources.Comment: To appear in a JPhys special issue on molecular motor

Localization of Denaturation Bubbles in Random DNA Sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations.Comment: TeX file with postscript figure

Phase Transition in Two Species Zero-Range Process

We study a zero-range process with two species of interacting particles. We show that the steady state assumes a simple factorised form, provided the dynamics satisfy certain conditions, which we derive. The steady state exhibits a new mechanism of condensation transition wherein one species induces the condensation of the other. We study this mechanism for a specific choice of dynamics.Comment: 8 pages, 3 figure

Vortex pinning by a columnar defect in planar superconductors with point disorder

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.Comment: 12 pages, 5 figures, minor typos corrected, a new reference adde

Will jams get worse when slow cars move over?

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$ to perfect `laning'. We find that the system displays one large cluster (`jam') whose size increases with $b$, contrary to intuition. Even more remarkably, the lane `charge' (a measure for the number of particles in their preferred lane) exhibits a region of negative response: even though vehicles experience a stronger preference for the `right' lane, more of them find themselves in the `wrong' one! For $b$ very close to 1, a sharp transition restores a homogeneous state. Various characteristics of the system are computed analytically, in good agreement with simulation data.Comment: 7 pages, 3 figures; to appear in Europhysics Letters (2005

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)] emerges as a limiting case.Comment: 9 pages, 2 figure

Two-dimensional wetting with binary disorder: a numerical study of the loop statistics

We numerically study the wetting (adsorption) transition of a polymer chain on a disordered substrate in 1+1 dimension.Following the Poland-Scheraga model of DNA denaturation, we use a Fixman-Freire scheme for the entropy of loops. This allows us to consider chain lengths of order $N \sim 10^5$ to $10^6$, with $10^4$ disorder realizations. Our study is based on the statistics of loops between two contacts with the substrate, from which we define Binder-like parameters: their crossings for various sizes $N$ allow a precise determination of the critical temperature, and their finite size properties yields a crossover exponent $\phi=1/(2-\alpha) \simeq 0.5$.We then analyse at criticality the distribution of loop length $l$ in both regimes $l \sim O(N)$ and $1 \ll l \ll N$, as well as the finite-size properties of the contact density and energy. Our conclusion is that the critical exponents for the thermodynamics are the same as those of the pure case, except for strong logarithmic corrections to scaling. The presence of these logarithmic corrections in the thermodynamics is related to a disorder-dependent logarithmic singularity that appears in the critical loop distribution in the rescaled variable $\lambda=l/N$ as $\lambda \to 1$.Comment: 12 pages, 13 figure

Stochastic Ballistic Annihilation and Coalescence

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a q-deformed harmonic oscillator algebra.Comment: 4 pages RevTeX, 3 figures; revised version with some corrections, additional discussion and in RevTeX forma