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Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability

Quantum statistics --- Control theory --- Mathematical physics

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The book on Heavy-Fermion Systems is a part of the Book series ""Handbook of Metal Physics"", each volume of which is written to facilitate the research of Ph.D. students, faculty and other researchers in a specific area. The Heavy-Fermions (sometimes known as Heavy-Electrons) is a loosely defined collection of intermetallic compounds containing rare-earth (mostly Ce) or actinide (mostly U) elements. These unusual names were given due to the large effective mass (100-1,000 times greater than the mass of a free electron) below a critical temperature. They have a variety of ground states includi

Fermions. --- Metals --- Chemistry, Physical and theoretical. --- Physical metallurgy. --- Microstructure. --- Metallurgy --- Physics --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Physical metallurgy --- Fermi-Dirac particles --- Particles (Nuclear physics) --- Quantum statistics --- Interacting boson-fermion models --- Leptons (Nuclear physics)

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While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.

Chaotic behavior in systems. --- Dynamics. --- Statistical mechanics. --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Dynamical systems --- Kinetics --- Force and energy --- Physics --- Statics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Statistical methods

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The interaction between mathematics and mechanics is a never ending source of new developments. Today, challenging problems like space flight, gyroscope motions and tidal currents, can be studied on a laptop, feats that people still in the 1950’s dreamed of accomplishing. The present textbook addresses such problems and moreover, a wide-ranging spectrum of topics from bifurcation theory, optimization and control to rigid-body motion and continuum mechanics of elastic bodies and fluids. It fully encompasses the provision of mathematical tools up to their technical application. Because verifiability is a main element of science and numerical mathematics remain lackluster without demonstrations, a portion of the book is dedicated purely to computations. Due to space limitations the author has transferred this information to his homepage. For each of the covered topics the reader can practice mathematical experiments by using the assortment of Matlab-programs belonging to nearly each chapter. A concise program teaches many technical details in short form and data may be altered ad libitum (learning by doing). The reader will be able to produce each picture or diagram from the book by themselves. Recent Review of the German edition: "This book introduces the engineering-oriented reader to all the mathematical tools necessary for solving complex problems in the field of mechanics. The mathematics- oriented reader will find various applications of mathematical and numerical methods for modelling comprehensive mechanical-technical practical problems. Therefore this book will be interesting not only for students of various fields but also for practitioners, development engineers or mathematicians" (Hans Bufler, in: Zentralblatt MATH, 2007, Vol. 1100, Issue 2).

Engineering. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Mechanics. --- Computational intelligence. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Mathematics --- Numerical analysis. --- Statistical mechanics. --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Mechanics, applied. --- Mathematics. --- Computer science --- Classical Mechanics. --- Math --- Science