Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit $T \to 0$. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and sub-aging effects : our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the RSRG method to include systematic corrections to the previous zero temperature procedure via a series expansion in $T$. We then consider the generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the large scale effective model at low temperature does not depend on $\alpha$ in any dimension, so that the only observables sensitive to $\alpha$ are those that measure the `local persistence', such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in $d=2$ and obtain the two relevant time scales for aging properties.Comment: 33 pages, 3 eps figure

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

Localization properties of the anomalous diffusion phase x tμx ~ t^{\mu} in the directed trap model and in the Sinai diffusion with bias

We study the anomalous diffusion phase $x ~ t^{\mu}$ with $0<\mu<1$ which exists both in the Sinai diffusion at small bias, and in the related directed trap model presenting a large distribution of trapping time $p(\tau) \sim 1/\tau^{1+\mu}$. Our starting point is the Real Space Renormalization method in which the whole thermal packet is considered to be in the same renormalized valley at large time : this assumption is exact only in the limit $\mu \to 0$ and corresponds to the Golosov localization. For finite $\mu$, we thus generalize the usual RSRG method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows to compute exact series expansions in $\mu$ of all observables : at order $\mu^n$, it is sufficient to consider a spreading of the thermal packet onto at most $(1+n)$ traps in each sample, and to average with the appropriate measure over the samples. For the directed trap model, we show explicitly up to order $\mu^2$ how to recover the diffusion front, the thermal width, and the localization parameter $Y_2$. We moreover compute the localization parameters $Y_k$ for arbitrary $k$, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias, by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models.Comment: 33 pages, 3 eps figure

Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass (SG) in a field), in the universal regime of a large Imry Ma length so that coarsening of domains after a quench occurs over large scales. Two types of domain walls diffuse in opposite Sinai random potentials and mutually annihilate. The domain walls converge rapidly to a set of system-specific time-dependent positions {\it independent of the initial conditions}. We obtain the time dependent energy, magnetization and domain size distribution (statistically independent). The equilibrium limits agree with known exact results. We obtain exact scaling forms for two-point equal time correlation and two-time autocorrelations. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the spin glass are obtained. We compute the two-point two-time correlation which can be measured by experiments on spin-glass like systems. Thermal fluctuations are found to be dominated by rare events; all moments of truncated correlations are computed. The response to a small field applied after waiting time $t_w$, as measured in aging experiments, and the fluctuation-dissipation ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$, $\hat{\alpha} <1$, it equals its equilibrium value X=1, though time translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

Measurements of Ξ(1530)0{\Xi \left( 1530\right) ^{0}} and Ξ‾(1530)0{\overline{\Xi }\left( 1530\right) ^{0}} production in proton–proton interactions at sNN\sqrt{s_{NN}} = 17.3 = 17.3 GeV \text{ GeV } in the NA61/SHINE experiment

Double-differential yields of $\Xi\left(1530\right)^{0}$ and $\overline{\Xi}\left(1530\right)^{0}$ resonances produced in \pp interactions were measured at a laboratory beam momentum of 158~\GeVc. This measurement is the first of its kind in \pp interactions below LHC energies. It was performed at the CERN SPS by the \NASixtyOne collaboration. Double-differential distributions in rapidity and transverse momentum were obtained from a sample of 26$\cdot$10$^6$ inelastic events. The spectra are extrapolated to full phase space resulting in mean multiplicity of $\Xi\left(1530\right)^{0}$ (6.73 $\pm$ 0.25 $\pm$ 0.67)$\times10^{-4}$ and $\overline{\Xi}\left(1530\right)^{0}$ (2.71 $\pm$ 0.18 $\pm$ 0.18)$\times10^{-4}$. The rapidity and transverse momentum spectra and mean multiplicities were compared to predictions of string-hadronic and statistical model calculations

Measurements of Ξ−{\Xi }{^-} and Ξ‾+\overline{\Xi }{^+} production in proton–proton interactions at sNN\sqrt{s_{NN}}=17.3 GeV = 17.3 GeV in the NA61/SHINE experiment

International audienceThe production of $\Xi (1321)^{-}$ and $\overline{\Xi }(1321)^{+}$ hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 $\hbox {Ge}\hbox {V}\!/\!c$. Double differential distributions in rapidity ${y}$ and transverse momentum $p_{T}$ are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both ${\Xi }{^-}$ and $\overline{\Xi }{^+}$. The rapidity and transverse momentum spectra are compared to transport model predictions. The ${\Xi }{^-}$ mean multiplicity in inelastic p+p interactions at 158 $\hbox {Ge}\hbox {V}\!/\!c$ is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair

Modeling of the atomic ordering processes in Fe3Al intermetallics by the monte carlo simulation method combined with electronic theory of alloys

The evolution of atomic ordering processes in Fe3Al has been modeled by the Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitude of atomic ordering energies of atomic pairs in the Fe3Al system has been calculated by means of electronic theory in pseudopotential approximation up to sixth coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg–Williams long-range order (LRO) and Cowley–Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of MC simulation for each predefined temperature and Al concentration levels, which reveal the evolution of the system from DO3 → B2 → disordered state as temperature increases. The variation of ordering parameters with temperature has identified the transition temperature from DO3 → B2 type superlattice, and from B2 → disordered (a) solid solution at about 540 °C and .900 °C, respectively, showing good qualitative agreement with experimental results. The results of the present study imply that combination of electronic theory of alloys in pseudopotential approximation with MC simulation can be successfully applied for qualitative or semiquantitative analysis of energetical and structural characteristics of atomic ordering processes in Fe3Al intermetallics