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Transport Properties in Non-Equilibrium and Anomalous Systems
The study of fluctuations in statistical physics has a long history, and a general theory is well established, connecting fluctuations to response properties of equilibrium systems. Remarkably, this framework fails as soon as some current is flowing across the system, driving it out of equilibrium. The presence of currents is quite common in nature and produces rich phenomena which are far from being included in a general framework. This thesis focuses on this general problem by studying different models such as granular materials and systems exhibiting anomalous diffusion and shows how the generalized response techniques can be successfully used to catch the relevant degrees of freedom that drive the systems out of equilibrium. This study paves the way to the use of the generalized fluctuation relations in an operative way, in order to extract information from a non-equilibrium system and to build the corresponding phenomenological theory.
Introduction to Random Matrices
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Transport and Fluctuations in Granular Fluids
This brief offers a concise presentation of granular fluids from the point of view of non-equilibrium statistical physics. The emphasis is on fluctuations, which can be large in granular fluids due to the small system size (the number of grains is many orders of magnitude smaller than in molecular fluids). Firstly, readers will be introduced to the most intriguing experiments on fluidized granular fluids. Then granular fluid theory, which goes through increasing levels of coarse-graining and emerging collective phenomena, is described. Problems and questions are initially posed at the level of kinetic theory, which describes particle densities in full or reduced phase-space. Some answers bec...
Large Deviations in Physics
This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.
Probabilità in Fisica
Questo testo, che nasce dall'esperienza didattica degli autori, si propone di introdurre gli aspetti fondamentali della teoria della probabilità e dei processi stocastici, guardando con particolare attenzione alle connessioni con la meccanica statistica, il caos, le applicazioni modellistiche ed i metodi numerici. La prima parte è costituita da un'introduzione generale alla probabilità con particolare enfasi sulla probabilità condizionata, le densità marginali e i teoremi limite. Nella seconda parte, prendendo spunto dal moto Browniano, sono presentati i concetti fondamentali dei processi stocastici (catene di Markov, equazione di Fokker- Planck). La terza parte è una selezione di argomenti avanzati che possono essere trattati in corsi della laurea specialistica.
Storie e protagonisti della matematica italiana
20 anni fa – anzi qualcuno in più – iniziava le sue pubblicazioni “Lettera Matematica PRISTEM”, espressione di un gruppo di ricerca della “Bocconi” cui aderiscono anche docenti e studiosi di altre Università. La “Lettera” ha rappresentato un tentativo coraggioso di svecchiare la comunicazione matematica, di renderla meno accademica e più giornalistica con l’uso delle immagini, del colore e di un linguaggio diretto. Un tentativo di inserire la Matematica nei più ampi processi che riguardano la scuola e la società. In questo libro, i tre direttori della rivista sfogliano le sue annate per ricordare storie e personaggi (matematici e non) attorno a cui la “Lettera” è ...
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Institutional Diversity in Self-Governing Societies
The work of Elinor and Vincent Ostrom represents a distinctive contribution to the study of political economy, public policy and administration, collective action, and governance theory. Efforts to present a comprehensive overview of the Bloomington School that grew around the Workshop in Political Theory and Policy Analysis (now renamed the Ostrom Workshop), which they founded more than 40 years ago, received new impetus with the award of the Nobel Memorial Prize in Economic Science to Elinor Ostrom in 2009. Since then, renewed attempts have been made to map the Ostroms’ contributions to theories of polycentric governance and collective action, and to multi-methods and comparative institu...
The Constantinian Order of Saint George
According to legend the Constantinian Order is the oldest chivalric institution, founded by Emperor Constantine the Great and governed by successive Byzantine Emperors and their descendants. While this chronology was supported by multiple writers even into the twentieth century, it has little historical basis. Nonetheless, the Angeli, Farnese and Bourbon families which held the Grand Mastership could legitimately claim Byzantine imperial descent, albeit in the female line, and the Order’s cross replicates that seen by Constantine in the vision recorded by both Lactantius and Eusebius, writing very soon after Maximian’s defeat at the battle of the Milvian Bridge. The Order’s emergence i...
