Bücher der Reihe CRM Series in Mathematical Physics

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first.

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019.

This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "e;Dyson processes"e;, and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.

This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.

This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics.

Therefore, imaging quantum dynamics is a new frontier of science requiring advanced mathematical approaches for analyzing and solving spatial and temporal multidimensional partial differential equations such as Time-Dependent Schroedinger Equations (TDSE) and Time-Dependent Dirac equations (TDDEs for relativistic phenomena).

Laser Filamentation

Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions.

This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.

Describes many physical phenomena, their analytic solutions, that in many cases are preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach provides a global knowledge of the solution, while the numerical approach is always local.

This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems.

Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions.

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first.

This authoritative book presents the basic knowledge and state-of-the-art techniques necessary to carry out investigations of the cardiovascular system using modeling and simulation.

This authoritative work presents the basic knowledge and state-of-the-art techniques necessary to carry out investigations of the cardiovascular system using modeling and simulation.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.

Solitons were discovered by John Scott Russel in 1834, and have interested scientists and mathematicians ever since. Topics covered include mathematical and numerical aspects of solitons, as well as applications of solitons to nuclear and particle physics, cosmology, and condensed-matter physics.

Therefore, imaging quantum dynamics is a new frontier of science requiring advanced mathematical approaches for analyzing and solving spatial and temporal multidimensional partial differential equations such as Time-Dependent Schroedinger Equations (TDSE) and Time-Dependent Dirac equations (TDDEs for relativistic phenomena).

Solitons were discovered by John Scott Russel in 1834, and have interested scientists and mathematicians ever since. Topics covered include mathematical and numerical aspects of solitons, as well as applications of solitons to nuclear and particle physics, cosmology, and condensed-matter physics.

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable