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Nonequilibrium Many-Body Theory of Quantum Systems
The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics.
eBook
Three New Classes of Solvable N-Body Problems of Goldfish Type with Many Arbitrary Coupling Constants
Three new classes of N-body problems of goldfish type are identified, with N an arbitrary positive integer ( N ≥ 2 ). These models are characterized by nonlinear Newtonian (“accelerations equal forces”) equations of motion describing N equal point-particles moving in the complex z-plane. These highly nonlinear equations feature many arbitrary coupling constants, yet they can be solved by algebraic operations. Some of these N-body problems are isochronous, their generic solutions being all completely periodic with an overall period T independent of the initial data (but quite a few of these solutions are actually periodic with smaller periods T / p with p a positive integer); other models are isochronous for an open region of initial data, while the motions for other initial data are not periodic, featuring instead scattering phenomena with some of the particles incoming from, or escaping to, infinity in the remote past or future.
Journal Article
Transport in multilayered nanostructures : the dynamical mean-field theory approach
\"Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and: Develops the formalism of many-body Green's functions using the equation-of-motion approach Applies DMFT to study transport in multilayered nanostructures, which is likely to be one of the most prominent applications of nanotechnology in the coming years Develops formalism first for the bulk and then for the inhomogeneous multilayered systems Describes in great detail the science behind the metal-insulator transition, electronic charge reconstruction, strongly correlated contributions to capacitance, and superconductivity Includes complete derivations and emphasizes how to carry out numerical calculations, including discussions of parallel programming algorithms Provides descriptions of the crossover from tunneling to thermally activated transport, of the properties of Josephson junctions with barriers tuned near the metal-insulator transition of thermoelectric coolers and power generators and of nonequilibrium extensions to determine current-voltage characteristics as applications of the theory A series of over 40 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field\"-- Provided by publisher.
Book
Global Mean-Motion Resonances: Part II—Laplace-like Phase Angles to Facilitate Libration Searches in Multiplanetary N-body Simulations
We describe a method of determining three-body and four-body Laplace-like phase angles with the potential to librate about a mean value in multiplanet extrasolar systems. Unlike in past searches of N-body results, this method relies on global mean-motion resonances (MMRs) and takes into consideration the location of the most massive planet that defines the 1:1 global MMR in each (sub)system. We compiled lists of potentially librating phase angles and prevalent MMRs in 35 real multibody systems, and we discuss their properties in conjunction with recent investigations of librations discovered in sophisticated N-body simulations. We hope that our results will facilitate systematic libration searches in dynamical models of compact systems with three or more orbiting bodies.
Journal Article
From Bloch oscillations to many-body localization in clean interacting systems
In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier–Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.
Journal Article
Fly me to the moon
When a leaf falls on a windy day, it drifts and tumbles, tossed
every which way on the breeze. This is chaos in action. In Fly
Me to the Moon, Edward Belbruno shows how to harness the same
principle for low-fuel space travel--or, as he puts it, \"surfing
the gravitational field.\"
Belbruno devised one of the most exciting concepts now being
used in space flight, that of swinging through the cosmos on the
subtle fluctuations of the planets' gravitational pulls. His idea
was met with skepticism until 1991, when he used it to get a stray
Japanese satellite back on course to the Moon. The successful
rescue represented the first application of chaos to space travel
and ushered in an emerging new field.
Part memoir, part scientific adventure story, Fly Me to the
Moon gives a gripping insider's account of that mission and of
Belbruno's personal struggles with the science establishment. Along
the way, Belbruno introduces readers to recent breathtaking
advances in American space exploration. He discusses ways to
capture and redirect asteroids; presents new research on the origin
of the Moon; weighs in on discoveries like 2003 UB313 (now named
Eris), a dwarf planet detected in the far outer reaches of our
solar system--and much more.
Grounded in Belbruno's own rigorous theoretical research but
written for a general audience, Fly Me to the Moon is for
anybody who has ever felt moved by the spirit of discovery.
eBook
Introduction to the Statistical Physics of Integrable Many-body Systems
Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.
eBook
Quantum simulations with ultracold atoms in optical lattices
Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom–based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.
Journal Article