This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts: Part One: Classical Dynamical Systems Addresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity. Includes a survey of the theory of simple perceptrons and their storage capacity. Part Two: Quantum Dynamical Systems Focuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems. Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom. Introduces a model of quantum perceptron whose storage capacity is computed and compared with the classical one. Part Three: Quantum Dynamical Entropies and Complexities Devoted to quantum dynamical entropies and algorithmic complexities. This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.
A closed sea geographically well-defined within its coastlines, rich in natural and human life. A concentration of Biodiversity in the broadest sense of the word: ecological diversity in nature and cultural diversity among men. A priceless treasure of the planet, this is the Adriatic. How to manage these places in order to preserve their peculiarities? A system of coastal and marine protected areas seems to be the only system that, despite everything, has been proving effective for more than a century. To systematize protected areas, to create a "Network", a network for sharing cultural exchanges and experiences and, above all, an ecological network. This is the challenge that awaits us in the short term. To make better the future of the Adriatic Sea.
Winner of the Strega Prize: A young girl in Tuscany finds hope amid heartbreak in “a story about the lonely daydreams of outsiders” (Kirkus Reviews). Smart, funny thirteen-year-old Luna lives in a small town on the coast of Tuscany. When her beloved brother, Luca, drowns in a surfing accident, Luna’s mother retreats into herself, while Luna believes that Luca still speaks to her through a whalebone washed up on the nearby shore. At school, stricken by her loss yet determined to carry on, Luna makes a new friend and ally, the eccentric Zot, a boy from Chernobyl. Luna’s fantasies will soon clash with the lies—even the well-intentioned ones—of the adult world, in this touching, funny, and imaginative novel by the celebrated author of Live Bait.
Benedetto Croce and Italian Fascism provides a unique analysis of the political life of the major Italian philosopher and literary figure Benedetto Croce (1866-1932). Drawing on a variety of resources rarely used before in Croce studies - including police documents, archival materials, and the private edition of Croce's diaries, the Taccuini, published in recent years - Fabio Rizi sheds new light on Croce and his influence throughout the Fascist era." "Tracing important events and influences in Croce's life, this biography clarifies misconceptions about his political contributions and his role in the resistance movement. Well-documented and insightful, Benedetto Croce and Italian Fascism offers a valuable contribution to Croce studies." --Book Jacket.
Un mare con le sue coste, raccolto, geograficamente ben delimitato, ricco di vita naturale e umana. Un concentrato di Biodiversità nel senso più esteso della parola: diversità ecologica in natura e diversità culturale tra gli uomini. Una ricchezza inestimabile del pianeta, questo è l'Adriatico. Come gestire questi luoghi per salvaguardarne le peculiarità? Quello delle aree protette, costiere e marine, appare essere l'unico sistema che, nonostante tutto, da più di un secolo, si sta rilevando efficace. Mettere a sistema le aree protette tra loro, creare un "Network", una rete di lavoro, di condivisione, di scambi culturali e di esperienze e, soprattutto, una rete ecologica, questa è la sfida che ci attende nel breve periodo. Per rendere migliore il futuro del mare Adriatico.
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
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