Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods which provide results only in the limit of vanishing drift. We show that on varying the drift, the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.Comment: 17 pages, two eps figures (included

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

Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function

It is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of two Bessel bridges, in which noncolliding condition is imposed. We show that the moments of the maximum value is then expressed using the double Dirichlet series, or using the integrals of products of the Jacobi theta functions and its derivatives. Since the present system will be provided as a diffusion scaling limit of a version of vicious walker model, the ensemble of 2-watermelons with a wall, the dominant terms in long-time asymptotics of moments of height of 2-watermelons are completely determined. For the height of 2-watermelons with a wall, the average value was recently studied by Fulmek by a method of enumerative combinatorics.Comment: v2: LaTeX, 19 pages, 2 figures, minor corrections made for publication in J. Stat. Phy

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

Quasicondensate and superfluid fraction in the 2D charged-boson gas at finite temperature

The Bogoliubov - de Gennes equations are solved for the Coulomb Bose gas describing a fluid of charged bosons at finite temperature. The approach is applicable in the weak coupling regime and the extent of its quantitative usefulness is tested in the three-dimensional fluid, for which diffusion Monte Carlo data are available on the condensate fraction at zero temperature. The one-body density matrix is then evaluated by the same approach for the two-dimensional fluid with e^2/r interactions, to demonstrate the presence of a quasi-condensate from its power-law decay with increasing distance and to evaluate the superfluid fraction as a function of temperature at weak coupling.Comment: 9 pages, 2 figure

Exactly solvable model of quantum diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.Comment: Submitted to J. Stat. Phy

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

Multi-layered Ruthenium-modified Bond Coats for Thermal Barrier Coatings

Diffusional approaches for fabrication of multi-layered Ru-modified bond coats for thermal barrier coatings have been developed via low activity chemical vapor deposition and high activity pack aluminization. Both processes yield bond coats comprising two distinct B2 layers, based on NiAl and RuAl, however, the position of these layers relative to the bond coat surface is reversed when switching processes. The structural evolution of each coating at various stages of the fabrication process has been and subsequent cyclic oxidation is presented, and the relevant interdiffusion and phase equilibria issues in are discussed. Evaluation of the oxidation behavior of these Ru-modified bond coat structures reveals that each B2 interlayer arrangement leads to the formation of α-Al 2 O 3 TGO at 1100°C, but the durability of the TGO is somewhat different and in need of further improvement in both cases

Existential Communication and Leadership

The aim of this article is to introduce and explain a number of important existentialist philosophers and concepts that we believe can contribute to a critical approach to leadership theory. Emphasis is placed on understanding the nature of communication from an existentialist perspective and so Jaspers' conceptualization of existential communication is introduced along with important related concepts that may be regarded as important facets of leader communication including Being-in-the-world, the Other, intersubjectivity, dialogue and indirect communication. Particular attention is paid to Buber's ideas on communication as relationship and dialogue. Throughout, reference is made to contemporary, and what is often regarded as orthodox, thinking regarding the centrality of communication to leadership practice as a means by which to highlight the salience of an existentialist analysis

Moments of vicious walkers and M\"obius graph expansions

A system of Brownian motions in one-dimension all started from the origin and conditioned never to collide with each other in a given finite time-interval $(0, T]$ is studied. The spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue-statistics of random Hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian orthogonal ensemble (GOE) statistics as the time $t$ is going on from 0 to $T$. In the present paper, we characterize this GUE-to-GOE transition by presenting the graphical expansion formula for the moments of positions of vicious walkers. In the GUE limit $t \to 0$, only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus. Following the time evolution of the vicious walkers, however, the graphs with twisted ribbons, called M\"obius graphs, increase their contribution to our expansion formula, and we have to deal with the topology of non-orientable surfaces. Application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the M\"obius expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function and references added. v.3: minor additions and corrections made for publication in Phys.Rev.