Glauber dynamics for the quantum Ising model in a transverse field on a regular tree

Motivated by a recent use of Glauber dynamics for Monte-Carlo simulations of path integral representation of quantum spin models [Krzakala, Rosso, Semerjian, and Zamponi, Phys. Rev. B (2008)], we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph $G$. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when $G$ is a regular $b$-ary tree and prove the same fast mixing results established in [Martinelli, Sinclair, and Weitz, Comm. Math. Phys. (2004)] for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the "cavity equation") together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space

Kinetically constrained spin models on trees

We analyze kinetically constrained 0-1 spin models (KCSM) on rooted and unrooted trees of finite connectivity. We focus in particular on the class of Friedrickson-Andersen models FA-jf and on an oriented version of them. These tree models are particularly relevant in physics literature since some of them undergo an ergodicity breaking transition with the mixed first-second order character of the glass transition. Here we first identify the ergodicity regime and prove that the critical density for FA-jf and OFA-jf models coincide with that of a suitable bootstrap percolation model. Next we prove for the first time positivity of the spectral gap in the whole ergodic regime via a novel argument based on martingales ideas. Finally, we discuss how this new technique can be generalized to analyze KCSM on the regular lattice $\mathbb{Z}^d$.Comment: Published in at http://dx.doi.org/10.1214/12-AAP891 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hydrodynamic limit of a disordered lattice gas

We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove the almost sure existence of the hydrodynamical limit in dimension d>2. The limit equation is a non linear diffusion equation with diffusion matrix characterized by a variational principle

A possible theoretical explanation of metallicity gradients in elliptical galaxies

Models of chemical evolution of elliptical galaxies taking into account different escape velocities at different galactocentric radii are presented. As a consequence of this, the chemical evolution develops differently in different galactic regions; in particular, we find that the galactic wind, powered by supernovae (of type II and I) starts, under suitable conditions, in the outer regions and successively develops in the central ones. The rate of star formation (SFR) is assumed to stop after the onset of the galactic wind in each region. The main result found in the present work is that this mechanism is able to reproduce metallicity gradients, namely the gradients in the $Mg_2$ index, in good agreement with observational data. We also find that in order to honor the constant [Mg/Fe] ratio with galactocentric distance, as inferred from metallicity indices, a variable initial mass function as a function of galactocentric distance is required. This is only a suggestion since trends on abundances inferred just from metallicity indices are still uncertain.Comment: 18 pages, LaTeX file with 4 figures using mn.sty, submitted to MNRA

The phase diagrams of iron-based superconductors: theory and experiments

Phase diagrams play a primary role in the understanding of materials properties. For iron-based superconductors (Fe-SC), the correct definition of their phase diagrams is crucial because of the close interplay between their crystallo-chemical and magnetic properties, on one side, and the possible coexistence of magnetism and superconductivity, on the other. The two most difficult issues for understanding the Fe-SC phase diagrams are: 1) the origin of the structural transformation taking place during cooling and its relationship with magnetism; 2) the correct description of the region where a crossover between the magnetic and superconducting electronic ground states takes place. Hence a proper and accurate definition of the structural, magnetic and electronic phase boundaries provides an extremely powerful tool for material scientists. For this reason, an exact definition of the thermodynamic phase fields characterizing the different structural and physical properties involved is needed, although it is not easy to obtain in many cases. Moreover, physical properties can often be strongly dependent on the occurrence of micro-structural and other local-scale features (lattice micro-strain, chemical fluctuations, domain walls, grain boundaries, defects), which, as a rule, are not described in a structural phase diagram. In this review, we critically summarize the results for the most studied 11-, 122- and 1111-type compound systems, providing a correlation between experimental evidence and theory

Logical Specification and Analysis of Fault Tolerant Systems through Partial Model Checking

This paper presents a framework for a logical characterisation of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modelled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform modelling scheme in which to specify a formal model of the system, its failing behaviour and possibly its fault-recovering procedures. Once a formal model is provided into our scheme, fault tolerance - with respect to a given property - can be formalized as an equational µ-calculus formula. This formula expresses in a logic formalism, all the fault scenarios satisfying that fault tolerance property. Such a characterisation understands the analysis of fault tolerance as a form of analysis of open systems and thank to partial model checking strategies, it can be made independent on any particular fault assumption. Moreover this logical characterisation makes possible the fault-tolerance verification problem be expressed as a general µ-calculus validation problem, for solving which many theorem proof techniques and tools are available. We present several analysis methods showing the flexibility of our approach

Relaxation time of LL-reversal chains and other chromosome shuffles

We prove tight bounds on the relaxation time of the so-called $L$-reversal chain, which was introduced by R. Durrett as a stochastic model for the evolution of chromosome chains. The process is described as follows. We have $n$ distinct letters on the vertices of the ${n}$-cycle (${{\mathbb{Z}}}$ mod $n$); at each step, a connected subset of the graph is chosen uniformly at random among all those of length at most $L$, and the current permutation is shuffled by reversing the order of the letters over that subset. We show that the relaxation time $\tau (n,L)$, defined as the inverse of the spectral gap of the associated Markov generator, satisfies $\tau (n,L)=O(n\vee \frac{n^3}{L^3})$. Our results can be interpreted as strong evidence for a conjecture of R. Durrett predicting a similar behavior for the mixing time of the chain.Comment: Published at http://dx.doi.org/10.1214/105051606000000295 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow

Suppression of the transient energy growth in subcritical plane Poiseuille flow via feedback control is addressed. It is assumed that the time derivative of any of the velocity components can be imposed at the walls as control input, and that full-state information is available. We show that it is impossible to design a linear state-feedback controller that leads to a closed-loop flow system without transient energy growth. In a subsequent step, full-state feedback controllers -- directly targeting the transient growth mechanism -- are designed, using a procedure based on a Linear Matrix Inequalities approach. The performance of such controllers is analyzed first in the linear case, where comparison to previously proposed linear-quadratic optimal controllers is made; further, transition thresholds are evaluated via Direct Numerical Simulations of the controlled three-dimensional Poiseuille flow against different initial conditions of physical interest, employing different velocity components as wall actuation. The present controllers are effective in increasing the transition thresholds in closed loop, with varying degree of performance depending on the initial condition and the actuation component employed

The value of novelty in schizophrenia

Influential models of schizophrenia suggest that patients experience incoming stimuli as excessively novel and motivating, with important consequences for hallucinatory experience and delusional belief. However, whether schizophrenia patients exhibit excessive novelty value and whether this interferes with adaptive behaviour has not yet been formally tested. Here, we employed a three-armed bandit task to investigate this hypothesis. Schizophrenia patients and healthy controls were first familiarised with a group of images and then asked to repeatedly choose between familiar and unfamiliar images associated with different monetary reward probabilities. By fitting a reinforcement-learning model we were able to estimate the values attributed to familiar and unfamiliar images when first presented in the context of the decision-making task. In line with our hypothesis, we found increased preference for newly introduced images (irrespective of whether these were familiar or unfamiliar) in patients compared to healthy controls and this to correlate with severity of hallucinatory experience. In addition, we found a correlation between value assigned to novel images and task performance, suggesting that excessive novelty value may interfere with optimal learning in patients, putatively through the disruption of the mechanisms regulating exploration versus exploitation. Our results suggest excessive novelty value in patients, whereby even previously seen stimuli acquire higher value as the result of their exposure in a novel context – a form of ‘hyper novelty’ which may explain why patients are often attracted by familiar stimuli experienced as new