This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.
The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.
This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.
The bloody battle fought on 15 August 1702 on the banks of the Po marked the beginning of a bloody struggle that lasted until 1706, which did not spare the cities and saw the active participation of the populations involved. The author turns his attention to the events leading up to the battle and the composition of the armies involved, with particular attention to that of the state of Milan, partly composed of officers and soldiers from the peninsula. The reconstruction of the situation on the field is very meticulous, carried out through the use of sources that are also difficult to find. It is worth noting the accurate study of the state of the places at the time of the battle, which today is no longer comparable to that of 1702, due to the alterations that the course of the Po has undergone over time and the human activity and settlements that have taken place: without it, it would not be easy to understand the movements of the troops in the area and the course of the battle itself. In this book, Fabio Fiorentin has been able to capture the different aspects of one of the most significant moments of the War of Spanish Succession in Italy, culminating in the famous siege of Turin in 1706 and ending with the defeat of the Franco-Spanish armies forced to abandon the peninsula. In it, instead of the Spanish, a strong imperial (or rather Austrian) dominance was established, which between various vicissitudes and the Napoleonic parenthesis, characterised Italian history for the next 150 years. Fiorentin also extends his research to the events that occurred after the battle and their consequences on the course of the war, which leaves us looking forward to his further studies on this period.
The idea of editing the present volume in the Lecture Notes in Physics series arosewhileorganizingthe“ConferenceonIrreversibleQuantumDynamics”that took place at The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from July 29 to August 2, 2002. The aim of the Conference was to bring together di?erent groups of - searcherswhoseinterestsandpursuitsinvolveirreversibilityandtimeasymmetry in quantum mechanics. The Conference promoted open and in-depth exchanges of di?erent points of view, concerning both the content and character of qu- tum irreversibility and the methodologies used to study it. The following main themes were addressed: • Theoretical Aspects of Quantum Irreversible Dynamics • Open Quantum Systems and Applications • Foundational Aspects of Irreversible Quantum Dynamics • Asymmetric Time Evolution and Resonances Eachthemewasreviewedbyanexpertinthe?eld,accompaniedbymorespeci?c, research-like shorter talks. The whole topic of quantum irreversibility in all its manifold aspects has always raised a lot of interest, starting with the description of unstable systems in quantum mechanics and the issue of quantum measurement. Further, in - cent years a boost of activity concerning noise, dissipation and open systems has been prompted by the fast developing ?eld of quantum communication and information theory. These considerations motivated the editors to put together a volume that tries to summarize the present day status of the research in the ?eld, with the aim of providing the reader with an accessible and exhaustive introduction to it.
The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.
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