Large deviations in quantum lattice systems: one-phase region

We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions and general observables, both in the high temperature regime and in dimension one.Comment: 30 pages, LaTeX 2

More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure

Edmund Burke and the issue of a conservative and liberal tradition in Italy, 1791-1945.

To synthesise, by means of a metaphor, Edmund Burke’s acceptance in Italy, we must imagine him as the silent guest whose weighty presence upset the political thought of many writers. I use the expression “silent guest” because most of the writers who used his rhetoric abstained from quoting their source and from explicitly stating that it was Burke. To explain this reluctance, we must widen our gaze to consider, more broadly, the understanding of Burke’s political thought, which, over time, has generated entirely opposite views. That is to say that scholars have found reasons both to enhance Burke’s reputation as a reactionary while also fostering the idea that he was a modern liberal. Hence, the fear of those who quoted him of being misunderstood and considered as members of one of two opposing coalitions that they were not part of

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure

Escape Orbits for Non-Compact Flat Billiards

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos

An infinite step billiard

A class of non-compact billiards is introduced, namely the infinite step billiards, i.e. systems of a point particle moving freely in the domain Ω = ∪n∈ℕ[n,n + 1] × [0, p_n], with elastic reflections on the boundary; here p_0 = 1, p_n > 0 and pn ↘ 0. After describing some generic ergodic features of these dynamical systems, we turn to a more detailed study of the example p_n = 2^{-n}. Playing an important role in this case are the so-called escape orbits, that is, orbits going to +∞ monotonically in the X-velocity. A fairly complete description of them is given. This enables us to prove some results concerning the topology of the dynamics on the billiard

Modal parameters identification with environmental tests and advanced numerical analyses for masonry bell towers: a meaningful case study

Abstract In the first part, a dynamic monitoring for non-destructive evaluation of heritage structures is discussed with reference to a case study, namely the Pomposa Abbey belfry, located in the Ferrara Province (Italy). The main dynamic parameters constitute an important reference to define an advanced numerical model, discussed in the second part, based on Non-Smooth Contact Dynamics (NSCD) method. Schematised as a system of rigid blocks undergoing frictional sliding and plastic impacts, the tower has exhibited complex dynamics, because of both geometrical nonlinearity and the non-smooth nature of the contact laws. First, harmonic oscillations have been applied to the basement of the tower and a systematic parametric study has been conducted, aimed at correlating the system vulnerability to the values of amplitude and frequency of the assigned excitation corroborated by the dynamic identification results. In addition, numerical analyses have been done to highlight the effects of the friction coefficient and of the blocks geometries on the dynamics, in particular on the collapse modes. Finally, a study of the tower stability against seismic excitations has been addressed and 3D simulations have been performed with a real earthquake

Limit theorems for Lévy flights on a 1D Lévy random medium

We study a random walk on a point process given by an ordered array of points (ωk, k ∈ Z) on the real line. The distances ωk+1 − ωk are i.i.d. random variables in the domain of attraction of a β-stable law, with β ∈ (0, 1) ∪ (1, 2). The random walk has i.i.d. jumps such that the transition probabilities between ωk and ωℓ depend on ℓ − k and are given by the distribution of a Z-valued random variable in the domain of attraction of an α-stable law, with α ∈ (0, 1) ∪ (1, 2). Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a Lévy flight on a Lévy random medium. For all combinations of the parameters α and β, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not càdlàg, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology

iconic crumbling of the clock tower in amatrice after 2016 central italy seismic sequence advanced numerical insight

Abstract The present paper investigates from an advanced numerical point of view the progressive damage of the Amatrice (Rieti, Italy) civic clock tower, after a long sequence of strong earthquakes that struck central Italy in 2016. Two advanced numerical models are here utilised to have an insight into the modalities of progressive damage and the behaviour of the structure under strong non-linear dynamic excitations, namely a Non-Smooth Contact Dynamics (NSCD) and a FE Concrete Damage Plasticity (CDP) models. In both cases, a full 3D detailed discretization is adopted. From the numerical results, both the role played by the actual geometries and the insufficient resistance of the constituent materials are envisaged, showing a good match with actual crack patterns observed after the seismic sequence

On infinite-volume mixing

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, testing them on a prototypical class of infinite measure-preserving dynamical systems, namely, the random walks.Comment: 34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous version was partially incorrect