Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures

According to recent progress in the finite size scaling theory of critical disordered systems, the nature of the phase transition is reflected in the distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. In this paper, we apply this analysis to the delocalization transition of an heteropolymeric chain at a selective fluid-fluid interface. The width $\Delta T_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ are found to decay with the same exponent $L^{-1/\nu_{R}}$, where $1/\nu_{R} \sim 0.26$. The distribution of pseudo-critical temperatures $T_c(i,L)$ is clearly asymmetric, and is well fitted by a generalized Gumbel distribution of parameter $m \sim 3$. We also consider the free energy distribution, which can also be fitted by a generalized Gumbel distribution with a temperature dependent parameter, of order $m \sim 0.7$ in the critical region. Finally, the disorder averaged number of contacts with the interface scales at $T_c$ like $L^{\rho}$ with $\rho \sim 0.26 \sim 1/\nu_R$.Comment: 9 pages,6 figure

Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences

The adsorption of an ideal heteropolymer loop at a potential point well is investigated within the frameworks of a standard random matrix theory. On the basis of semi-analytical/semi-numerical approach the histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain's links is constructed. It is shown that the sequences having the transition points in the tail of the histogram display the correlations between nearest-neighbor monomers.Comment: 11 pages (revtex), 3 figure

Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space

We show that an appropriate description of the non-equilibrium dynamics of disordered systems is obtained through a strong disorder renormalization procedure in {\it configuration space}, that we define for any master equation with transitions rates $W ({\cal C} \to {\cal C}')$ between configurations. The idea is to eliminate iteratively the configuration with the highest exit rate $W_{out} ({\cal C})= \sum_{{\cal C}'} W ({\cal C} \to {\cal C}')$ to obtain renormalized transition rates between the remaining configurations. The multiplicative structure of the new generated transition rates suggests that, for a very broad class of disordered systems, the distribution of renormalized exit barriers defined as $B_{out} ({\cal C}) \equiv - \ln W_{out}({\cal C})$ will become broader and broader upon iteration, so that the strong disorder renormalization procedure should become asymptotically exact at large time scales. We have checked numerically this scenario for the non-equilibrium dynamics of a directed polymer in a two dimensional random medium.Comment: v2=final versio

Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules

We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in finite-size systems without simulating the actual time evolution which can be extremely slow, we propose to focus on first-passage times that satisfy 'backward master equations'. Upon the iterative elimination of configurations, we obtain the exact renormalization rules that can be followed numerically. To test this approach, we study the statistics of some first-passage times for two disordered models : (i) for the random walk in a two-dimensional self-affine random potential of Hurst exponent $H$, we focus on the first exit time from a square of size $L \times L$ if one starts at the square center. (ii) for the dynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, we consider the first passage time $t_f$ to zero-magnetization when starting from a fully magnetized configuration. Besides the expected linear growth of the averaged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaled distribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large $u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simply interpreted in terms of rare events if the sample-to-sample fluctuation exponent for the barrier is $\psi_{width}=1/3$.Comment: 8 pages, 4 figure

Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?

The motion of driven interfaces in random media at finite temperature $T$ and small external force $F$ is usually described by a linear displacement $h_G(t) \sim V(F,T) t$ at large times, where the velocity vanishes according to the creep formula as $V(F,T) \sim e^{-K(T)/F^{\mu}}$ for $F \to 0$. In this paper, we question this picture on the specific example of the directed polymer in a two dimensional random medium. We have recently shown (C. Monthus and T. Garel, arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point". In the present paper, we obtain that for small $F$, this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power-law $P(\tau) \sim 1/\tau^{1+\alpha}$, where the exponent $\alpha(F,T)$ vanishes as $\alpha(F,T) \propto F^{\mu}$ as $F \to 0$. Our conclusion is that in the small force region $\alpha(F,T)<1$, the divergence of the averaged trapping time $\bar{\tau}=+\infty$ induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sub-linearly in time $h_G(t) \sim t^{\alpha(F,T)}$, i.e. the asymptotic velocity vanishes V=0. This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value $\zeta_{eq}=2/3$ up to some large scale, becomes equal to $\zeta=1$ at the largest scales.Comment: v3=final versio

The UV, Lyman α, and dark matter halo properties of high-redshift galaxies

We explore the properties of high-redshift Lyman alpha emitters (LAEs), and their link with the Lyman-break galaxy (LBG) population, using a semi-analytic model of galaxy formation that takes into account resonant scattering of Lyα photons in gas outflows. We can reasonably reproduce the abundances of LAEs and LBGs from z≈3 to 7, as well as most UV luminosity functions (LFs) of LAEs. The stronger dust attenuation for (resonant) Lyα photons compared to UV continuum photons in bright LBGs provides a natural interpretation to the increase of the LAE fraction in LBG samples, XLAE, towards fainter magnitudes. The redshift evolution of XLAE seems however very sensitive to UV magnitudes limits and equivalent width (EW) cuts. In spite of the apparent good match between the statistical properties predicted by the model and the observations, we find that the tail of the Lyα EW distribution (EW≳100 Å) cannot be explained by our model, and we need to invoke additional mechanisms. We find that LAEs and LBGs span a very similar dynamical range, but bright LAEs are ∼4times rarer than LBGs in massive haloes. Moreover, massive haloes mainly contain weak LAEs in our model, which might introduce a bias towards low-mass haloes in surveys which select sources with high-EW cuts. Overall, our results are consistent with the idea that LAEs and LBGs make a very similar galaxy population. Their apparent differences seem mainly due to EW selections, UV detection limits, and a decreasing Lyα to UV escape fraction ratio in high star formation rate galaxie

From Collapse to Freezing in Random Heteropolymers

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H --> 0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H < 1, entropy approaches zero as N --> infty (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ N^nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis. Submitted to Europhys.Let

Lattice model for cold and warm swelling of polymers in water

We define a lattice model for the interaction of a polymer with water. We solve the model in a suitable approximation. In the case of a non-polar homopolymer, for reasonable values of the parameters, the polymer is found in a non-compact conformation at low temperature; as the temperature grows, there is a sharp transition towards a compact state, then, at higher temperatures, the polymer swells again. This behaviour closely reminds that of proteins, that are unfolded at both low and high temperatures.Comment: REVTeX, 5 pages, 2 EPS figure

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums

For Anderson tight-binding models in dimension $d$ with random on-site energies $\epsilon_{\vec r}$ and critical long-ranged hoppings decaying typically as $V^{typ}(r) \sim V/r^d$, we show that the strong multifractality regime corresponding to small $V$ can be studied via the standard perturbation theory for eigenvectors in quantum mechanics. The Inverse Participation Ratios $Y_q(L)$, which are the order parameters of Anderson transitions, can be written in terms of weighted L\'evy sums of broadly distributed variables (as a consequence of the presence of on-site random energies in the denominators of the perturbation theory). We compute at leading order the typical and disorder-averaged multifractal spectra $\tau_{typ}(q)$ and $\tau_{av}(q)$ as a function of $q$. For $q<1/2$, we obtain the non-vanishing limiting spectrum $\tau_{typ}(q)=\tau_{av}(q)=d(2q-1)$ as $V \to 0^+$. For $q>1/2$, this method yields the same disorder-averaged spectrum $\tau_{av}(q)$ of order $O(V)$ as obtained previously via the Levitov renormalization method by Mirlin and Evers [Phys. Rev. B 62, 7920 (2000)]. In addition, it allows to compute explicitly the typical spectrum, also of order $O(V)$, but with a different $q$-dependence $\tau_{typ}(q) \ne \tau_{av}(q)$ for all $q>q_c=1/2$. As a consequence, we find that the corresponding singularity spectra $f_{typ}(\alpha)$ and $f_{av}(\alpha)$ differ even in the positive region $f>0$, and vanish at different values $\alpha_+^{typ} > \alpha_+^{av}$, in contrast to the standard picture. We also obtain that the saddle value $\alpha_{typ}(q)$ of the Legendre transform reaches the termination point $\alpha_+^{typ}$ where $f_{typ}(\alpha_+^{typ})=0$ only in the limit $q \to +\infty$.Comment: 13 pages, 2 figures, v2=final versio