Strongly Interacting Quantum Systems Out Of Equilibrium

Over the last decade new experimental tools and theoretical concepts are providing new insights into collective nonequilibrium behavior of quantum systems. The exquisite control provided by laser trapping and cooling techniques allows us to observe the behavior of condensed bose and degenerate Fermi gases under nonequilibrium drive or after `quenches' in which a Hamiltonian parameter is suddenly or slowly changed. On the solid state front, high intensity short-time pulses and fast (femtosecond) probes allow solids to be put into highly excited states and probed before relaxation and dissipation occur. Experimental developments are matched by progress in theoretical techniques ranging from exact solutions of strongly interacting nonequilibrium models to new approaches to nonequilibrium numerics. The summer school `Strongly interacting quantum systems out of equilibrium' held at the Les Houches School of Physics as its XCIX session was designed to summarize this progress, lay out the open questions and define directions for future work. This books collects the lecture notes of the main courses given in this summer school.

Over the last decade new experimental tools and theoretical concepts are providing new insights into collective nonequilibrium behaviour of quantum systems. On the solid state front, high intensity short-timepulses and fast (femtosecond) probes allow solids to be put into highly excited states and probed before relaxation and dissipation occur. Experimental developments are matched by progress in theoretical techniques ranging from exact solutions of strongly interacting nonequilibrium models to newapproaches to nonequilibrium numerics. The summer school held at the Les Houches School of Physics as its XCIX session was designed to summarise this progress, lay out the open questions and define directions for future work. This books collects the lecture notes of the main courses given in this summer school.

This book presents new experimental tools and theoretical concepts of collective nonequilibrium behavior of quantum systems. The book is based on the Les Houches Summer School of August 2012, "Strongly interacting quantum systems out of equilibrium".

And non-trivially predictable in the XY chain.

This thesis dissertation concerns the quantum dynamics of strongly interacting many-body systems under several non-equilibrium scenarios. Mimicking many real life settings, and specially some current major experiments, during most of this work we will deal with symmetrical interactions among the components, which will generate collective dynamics with high degree of correlation. The focus all throughout this work has been on the posssibility of accurately control the quantum properties of the system, even at the microscopic level, by cleverly choosing macroscopic manipulation protocols. Our main results can be summarized as follows. First, we thoroughly investigate the irreversible defect formation when the Dicke model, a paradigmatic light-matter system, is made to cross its quantum phase transition (QPT). Furthermore, we have been able to explain this dynamical QPT for totally connected lattices, which had remained unresolved by well-known theories like the Kibble-Zurek mechanism. This was done by means of a broad encompassing critical function theory. Also, by going beyond semi-adiabatic evolutions, we have discovered that the dynamical QPT of the Dicke model has an intermediate regime where non-equilibrium process provide a huge enhancing of quantum properties, far beyond the capabilities of equilibrium, quasi-equilibrium, or sudden quench schemes. Finally, we provided theoretical evidence and insights for the possibilities of quantum magnetism interactions in current high precision alkaline earth atom lattice clocks.

This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.

This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.