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Many-body theory stands at the foundation of modern quantum statistical mechanics. It is introduced here to graduate students in physics, chemistry, engineering and biology. The book provides a contemporary understanding of irreversibility, particularly in quantum systems. It explains entropy production in quantum kinetic theory and in the master equation formulation of non-equilibrium statistical mechanics. The first half of the book focuses on the foundations of non-equilibrium statistical mechanics with emphasis on quantum mechanics. The second half of the book contains alternative views of quantum statistical mechanics, and topics of current interest for advanced graduate level study and research. Unique to textbooks on this subject, this book contains a discussion of the fundamental Gleason theorem. Quantum entanglements are treated in application to quantum computation and the difficulties arising from decoherence. The relativistic generalization of the Boltzmann equation is derived, and modern transport applications to reservoir ballistic transport are developed.

Statistical physics --- Quantum statistics. --- Statistique quantique --- Statistical mechanics. --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Thermodynamics --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics

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In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles. Contents: On the Theory of Superfluidit

Quantum statistics. --- Statistical mechanics. --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics

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This book deals with the statistical theory of strongly coupled Coulomb systems. After an elementary introduction to the physics of nonideal plasmas, a presentation of the method of (nonequilibrium) Green's functions is given. On this basis, the dielectric, thermodynamic, transport, and relaxation properties are discussed systematically. Especially, the behavior of bound states in the surrounding plasma (lowering of the ionization energy), the ionization kinetics, and the equation of state of dense partially ionized hydrogen are each carefully investigated. Furthermore, generalized kinetic equations are derived which are also valid for short time scales. They are applied to ultra-fast processes and to plasmas in laser fields.

Plasma (Ionized gases) --- Quantum statistics. --- Transport theory. --- Statistical thermodynamics. --- Quantum theory --- Statistical mechanics --- Statistical physics --- Thermodynamics --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Quantum statistical mechanics --- Matrix mechanics --- Wave mechanics --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases

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This book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova. The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.

Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Quantum physics. --- Statistical Physics. --- Gravitation. --- Atoms. --- Molecules. --- Quantum statistics. --- Quantum Physics. --- Gravitational Physics. --- Atomic, Molecular and Chemical Physics. --- Quantum Gases and Condensates. --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematical statistics --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics --- Chemistry, Physical and theoretical --- Stereochemistry --- Properties --- Statistical methods --- Constitution

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This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on other courses he has given over the last two decades.

Quantum theory. --- Differentiable dynamical systems. --- Quantum statistics. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Statistical physics. --- Complex Systems. --- Quantum Physics. --- Mathematical Physics. --- Quantum Optics. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Statistical methods --- Dynamical systems. --- Quantum physics. --- Mathematical physics. --- Quantum optics. --- Optics --- Photons --- Quantum theory --- Physical mathematics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics