Classical, Discrete Spin Models
Author: H. Moraal
Publisher:
Published: 2014-01-15
Total Pages: 268
ISBN-13: 9783662162408
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Lectures on Probability Theory and Statistics
Author: J. Bertoin
Publisher: Springer
Published: 2004-09-03
Total Pages: 296
ISBN-13: 354048115X
DOWNLOAD EBOOKPart I, Bertoin, J.: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- Lévy processes.- Occupation times of a linear Brownian motion.- Part II, Martinelli, F.: Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Part III, Peres, Yu.: Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- The Random Walks RW (lambda) .- Capacity.-.Intersection-Equivalence.- Reconstruction for the Ising Model on a Tree,- Unpredictable Paths in Z and EIT in Z3.- Tree-Indexed Processes.- Recurrence for Tree-Indexed Markov Chains.- Dynamical Pecsolation.- Stochastic Domination Between Trees.
Magnetic Excitations and Geometric Confinement
Author: Gary Matthew Wysin
Publisher: Iop Expanding Physics
Published: 2015
Total Pages: 0
ISBN-13: 9780750310758
DOWNLOAD EBOOKIn this book, author Gary Wysin provides an overview of model systems and their behaviour and effects, and is intended for advanced students and researchers in physics, chemistry and engineering interested in confined magnetics. It is also suitable as an auxiliary text in a class on magnetism or solid state physics. Previous physics knowledge is expected, along with some basic knowledge of classical electromagnetism and electromagnetic waves for the latter chapters.
Nonlinear Dynamics
Author: M. Daniel
Publisher: Alpha Science Int'l Ltd.
Published: 2000
Total Pages: 490
ISBN-13: 9788173193262
DOWNLOAD EBOOKContributed articles presented at the International Conference on Nonlinear Dynamics: Integrability and Chaos held at Bharathidasan University during 12-16 Feb., 1998. In honor of Prof. M. Lakshmanan.
Gibbs Measures on Cayley Trees
Author: Utkir A. Rozikov
Publisher: World Scientific
Published: 2013
Total Pages: 404
ISBN-13: 9814513385
DOWNLOAD EBOOKThe Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.
Classical, Discrete Spin Models
Author: Hendrik Moraal
Publisher: Springer Verlag
Published: 1984
Total Pages: 0
ISBN-13: 9780387138961
DOWNLOAD EBOOKStatistical Approach to Quantum Field Theory
Author: Andreas Wipf
Publisher: Springer Nature
Published: 2021-10-25
Total Pages: 568
ISBN-13: 3030832635
DOWNLOAD EBOOKThis new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Many-Body Boson Systems
Author: André F. Verbeure
Publisher: Springer
Published: 2010-11-25
Total Pages: 190
ISBN-13: 0857291092
DOWNLOAD EBOOKThis book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus. Bridging the gap between general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipative perturbations; and the surprising but general relation between general quantum fluctuations and boson systems. Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings students and researchers smoothly from general concepts to vivid applications.
Models of Quantum Matter
Author: Hans-Peter Eckle
Publisher:
Published: 2019
Total Pages: 732
ISBN-13: 0199678839
DOWNLOAD EBOOKThe book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.
Discrete Quantum Mechanics
Author: H. Thomas Williams
Publisher: Morgan & Claypool Publishers
Published: 2015-12-01
Total Pages: 137
ISBN-13: 1681741253
DOWNLOAD EBOOKAfter a quarter century of discoveries that rattled the foundations of classical mechanics and electrodynamics, the year 1926 saw the publication of two works intended to provide a theoretical structure to support new quantum explanations of the subatomic world. Heisenberg's matrix mechanics and Schrodinger’s wave mechanics provided compatible but mathematically disparate ways of unifying the discoveries of Planck, Einstein, Bohr and many others. Efforts began immediately to prove the equivalence of these two structures, culminated successfully by John von Neumann’s 1932 volume "Mathematical Foundations of Quantum Mechanics." This forms the springboard for the current effort. We begin with a presentation of a minimal set of von Neumann postulates while introducing language and notation to facilitate subsequent discussion of quantum calculations based in finite dimensional Hilbert spaces. Chapters which follow address two-state quantum systems (with spin one-half as the primary example), entanglement of multiple two-state systems, quantum angular momentum theory and quantum approaches to statistical mechanics. A concluding chapter gives an overview of issues associated with quantum mechanics in continuous infinite-dimensional Hilbert spaces.
