Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory
DOWNLOAD
Download Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory
DOWNLOAD
Author : J.-B. Bru
language : en
Publisher: Springer
Release Date : 2016-11-30
Lieb Robinson Bounds For Multi Commutators And Applications To Response Theory written by J.-B. Bru and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Science categories.
Lieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions.In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*-algebraic setting for lattice fermions, as well as the celebrated Lieb-Robinson bounds for commutators, are explained in detail, for completeness.
Mathematical And Computational Modelling Across The Scales
DOWNLOAD
Author : Pedro Diez
language : en
Publisher: Springer Nature
Release Date : 2025-06-25
Mathematical And Computational Modelling Across The Scales written by Pedro Diez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Computers categories.
Many physical and engineering systems deal with micro-, meso-, macro-, and multi-scale phenomena. The accurate description and the reliable simulation of such phenomena entail major challenges from the point of view of both mathematical modelling and computational engineering. This book covers a selection of challenges related to "Mathematical and Computational Modelling Across the Scales”, stemming from the lecture notes of the XX edition of the Jacques-Louis Lions Spanish-French School in Numerical Simulations in Physics & Engineering. The thematic focus is broad, encompassing mathematical models of complex physical problems, theoretical results on their derivation, and development of numerical methods for their efficient simulation. The contributions of the book include: uncertainty quantification for phenomena at different scales such as epidemic dynamics, medical imaging, and geophysical exploration; structural health monitoring integrating small-scale sensor data in large-scale computational models; frontier numerical methods for the simulation of geophysical and heliophysical dynamics accounting for multi-scale, heterogeneous media; multi-physics, multi-scale models for the mechanobiology of atheroma plaques formation; locomotion models for swimming at the micro-scale; mathematical foundations of quantum mechanics phenomena at the micro-scale. The book is addressed to scientists and engineers, from both academia and industry, interested in the mathematical modelling and numerical simulation of a variety of complex systems in physics and engineering characterised by multiple scales.
Mathematical Problems In Quantum Physics
DOWNLOAD
Author : Federico Bonetto
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-24
Mathematical Problems In Quantum Physics written by Federico Bonetto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics
DOWNLOAD
Author : Jean-Bernard Bru
language : en
Publisher: Springer Nature
Release Date : 2023-06-16
C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics written by Jean-Bernard Bru and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-16 with Science categories.
This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.
Adiabatic Perturbation Theory In Quantum Dynamics
DOWNLOAD
Author : Stefan Teufel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Adiabatic Perturbation Theory In Quantum Dynamics written by Stefan Teufel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Perturbation (Quantum dynamics) categories.
The Role Of Topology In Materials
DOWNLOAD
Author : Sanju Gupta
language : en
Publisher: Springer
Release Date : 2018-04-21
The Role Of Topology In Materials written by Sanju Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-21 with Science categories.
This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.
Operator Algebras And Quantum Statistical Mechanics 1
DOWNLOAD
Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-05-27
Operator Algebras And Quantum Statistical Mechanics 1 written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-27 with Mathematics categories.
This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.
Spaces And Identities In Border Regions
DOWNLOAD
Author : Christian Wille
language : en
Publisher: Transcript Verlag, Roswitha Gost, Sigrid Nokel u. Dr. Karin Werner
Release Date : 2015-05-15
Spaces And Identities In Border Regions written by Christian Wille and has been published by Transcript Verlag, Roswitha Gost, Sigrid Nokel u. Dr. Karin Werner this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-15 with Boundaries categories.
Spatial and identity research operates with differentiations and relations that are particularly useful for examining border regions in which social and geopolitical demarcations diverge. The authors of this volume investigate spatial and identity constructions in crossborder contexts as they appear in everyday, institutional, and media practices. The results are discussed with a keen eye for obliquely aligned spaces and identities linked to governmental issues of standardization and subjectivation. Research is based on empirical surveys conducted in Germany, France, Belgium, and Luxembourg.
The Statistical Mechanics Of Lattice Gases Volume I
DOWNLOAD
Author : Barry Simon
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
The Statistical Mechanics Of Lattice Gases Volume I written by Barry Simon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Science categories.
A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of high and low temperature expansions. The second volume will deal with the Peierls construction, infrared bounds, Lee-Yang theorems, and correlation inequality. This comprehensive work will be a useful reference not only to scientists working in mathematical statistical mechanics but also to those in related disciplines such as probability theory, chemical physics, and quantum field theory. It can also serve as a textbook for advanced graduate students. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Elementary Principles In Statistical Mechanics
DOWNLOAD
Author : Josiah Willard Gibbs
language : en
Publisher:
Release Date : 1902
Elementary Principles In Statistical Mechanics written by Josiah Willard Gibbs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1902 with Mechanics categories.