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Fluid mechanics --- Adhesion. --- Particles. --- Cold gases. --- Mathematical models.

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This book provides a pedagogical introduction to the concepts and methods of quantum field theory necessary for the study of condensed matter and ultracold atomic gases. After a thorough discussion of the basic methods of field theory and many-body physics (functional integrals, perturbation theory, Feynman diagrams, correlation functions and linear response theory, symmetries and their consequences, etc.), the book covers a wide range of topics, from electron gas and Fermi-liquid theory to superfluidity and superconductivity, magnetic instabilities in electron systems, and dynamical mean-field theory of Mott transition. The focus is on the study of model Hamiltonians, where the microscopic physics and characteristic energy scales are encoded into a few effective parameters, rather than first-principle methods which start from a realistic Hamiltonian at the microscopic level and then make material-specific predictions. The reader is expected to be familiar with elementary quantum mechanics and statistical physics, and some acquaintance with condensed-matter physics and ultracold gases may also be useful. No prior knowledge of field theory or many-body problem is required.

Cold gases. --- Condensed matter. --- Quantum field theory. --- Superconductivity. --- Superfluidity. --- Gaz. --- Basses températures. --- Matière condensée. --- Théorie quantique des champs. --- Superfluidité. --- Supraconductivité.

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A broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics and statistical mechanics --

Cold gases. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Gases --- Gaz --- Théorie quantique. --- Thermal properties --- Propriétés thermiques. --- Théorie quantique. --- Propriétés thermiques. --- Phase transformations (Statistical physics) --- Thermal properties.

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This book discusses non-equilibrium quantum many-body dynamics, recently explored in an analog quantum simulator of strongly correlated ultracold atoms. The first part presents a field-theoretical analysis of the experimental observability of the Higgs amplitude mode that emerges as a relativistic collective excitation near a quantum phase transition of superfluid Bose gases in an optical lattice potential. The author presents the dynamical susceptibilities to external driving of the microscopic parameters, taking into account a leading-order perturbative correction from quantum and thermal fluctuations and shows clear signatures of the Higgs mode in these observables. This is the first result that strongly supports the stability of the Higgs mode in three-dimensional optical lattices even in the presence of a spatially inhomogeneous confinement potential and paves the way for desktop observations of the Higgs mode. In the second part, the author applies the semi-classical truncated-Wigner approximation (TWA) to far-from-equilibrium quantum dynamics. Specifically, he considers the recent experiments on quantum-quench dynamics in a Bose-Hubbard quantum simulator. A direct comparison shows remarkable agreement between the numerical results from TWA and the experimental data. This result clearly indicates the potential of such a semi-classical approach in reliably simulating many-body systems using classical computers. The book also includes several chapters providing comprehensive reviews of the recent studies on cold-atomic quantum simulation and various theoretical methods, including the Schwinger-boson approach in strongly correlated systems and the phase-space semi-classical method for far-from-equilibrium quantum dynamics. These chapters are highly recommended to students and young researchers who are interested in semi-classical approaches in non-equilibrium quantum dynamics.

Cold gases. --- Ultracold neutrons. --- Quantum systems. --- Quantum theory --- System theory --- Ultra-cold neutrons --- Cold neutrons --- Gases --- Phase transformations (Statistical physics). --- Condensed materials. --- Superconductivity. --- Superconductors. --- Phase transitions (Statistical physics). --- Statistical physics. --- Quantum Gases and Condensates. --- Strongly Correlated Systems, Superconductivity. --- Phase Transitions and Multiphase Systems. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Statistical methods --- Materials

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The advent of laser cooling of atoms led to the discovery of ultra-cold matter, with temperatures below liquid Helium, which displays a variety of new physical phenomena. Physics of Ultra-Cold Matter gives an overview of this recent area of science, with a discussion of its main results and a description of its theoretical concepts and methods. Ultra-cold matter can be considered in three distinct phases: ultra-cold gas, Bose Einstein condensate, and Rydberg plasmas. This book gives an integrated view of this new area of science at the frontier between atomic physics, condensed matter, and plasma physics. It describes these three distinct phases while exploring the differences, as well as the sometimes unexpected similarities, of their respective theoretical methods. This book is an informative guide for researchers, and the benefits are a result from an integrated view of a very broad area of research, which is limited in previous books about this subject. The main unifying tool explored in this book is the wave kinetic theory based on Wigner functions. Other theoretical approaches, eventually more familiar to the reader, are also given for extension and comparison. The book considers laser cooling techniques, atom-atom interactions, and focuses on the elementary excitations and collective oscillations in atomic clouds, Bose-Einstein condensates, and Rydberg plasmas. Linear and nonlinear processes are considered, including Landau damping, soliton excitation and vortices. Atomic interferometers and quantum coherence are also included.

Cold gases. --- Bose-Einstein condensation. --- Rydberg states. --- Rydberg atoms --- Rydberg series --- Bose condensed fluids --- Bose condensed liquids --- Bose fluids --- Bose liquids --- Einstein condensation --- Laser cooling. --- Trapped ions. --- Ultracold neutrons. --- Ultracold neutrons --- Laser cooling --- Physics. --- Atoms. --- Matter. --- Phase transformations (Statistical physics). --- Condensed materials. --- Condensed matter. --- Plasma (Ionized gases). --- Low temperature physics. --- Low temperatures. --- Quantum Gases and Condensates. --- Low Temperature Physics. --- Plasma Physics. --- Atoms and Molecules in Strong Fields, Laser Matter Interaction. --- Atomic spectra --- Energy levels (Quantum mechanics) --- Bosons --- Condensation --- Superfluidity --- Gases --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Chemistry, Physical and theoretical --- Matter --- Stereochemistry --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases --- Cryogenics --- Low temperature physics --- Temperatures, Low --- Temperature --- Cold --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Solids --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Constitution