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Isochronous Systems

Francesco Calogero

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ... More


Fundamentals of Beam Physics

J. B. Rosenzweig

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198525547
eISBN:
9780191711725
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525547.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book presents beam physics using a unified approach, emphasizing basic concepts and analysis methods. While many existing resources in beams and accelerators are specialized to aid the ... More


Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A ... More


A Government for Free

Max. M Edling

in A Revolution in Favor of Government: Origins of the U.S. Constitution and the Making of the American State

Published in print:
2003
Published Online:
January 2005
ISBN:
9780195148701
eISBN:
9780199835096
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195148703.003.0014
Subject:
Political Science, American Politics

Shows how the Federalists responded to the Antifederalist objections to a stronger national government in the “fiscal‐military” sphere, thereby creating an understanding of the kind of state that was ... More


Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Alfonso Sorrentino

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.001.0001
Subject:
Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More


Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Vadim Kaloshin and Ke Zhang

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was ... More


ISOCHRONOUS HAMILTONIAN SYSTEMS ARE NOT RARE

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 5 various tricks are introduced, transforming Hamiltonian systems into isochronous Hamiltonian systems. The possibility to apply this procedure to large classes of Hamiltonian systems ... More


Order, Symmetry, and the Organization of Matter

Daniel L. Stein and Charles M. Newman

in Spin Glasses and Complexity

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691147338
eISBN:
9781400845637
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147338.003.0002
Subject:
Sociology, Science, Technology and Environment

This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and ... More


Spin Glasses: General Features

Daniel L. Stein and Charles M. Newman

in Spin Glasses and Complexity

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691147338
eISBN:
9781400845637
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147338.003.0005
Subject:
Sociology, Science, Technology and Environment

This chapter finally deals with the concept of spin glasses. The intention is not to provide anything approaching a thorough history of the subject. The field today is broad, with threads and ... More


Tonelli Lagrangians and Hamiltonians on Compact Manifolds

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter introduces the basic setting: Tonelli Lagrangians and Hamiltonians on a compact manifold. It discusses their main properties and some examples, and provides the opportunity to recall ... More


Practical Quantum Mechanics: Modern Tools and Applications

Efstratios Manousakis

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent ... More


Local Cauchy Problem

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter begins with a discussion of moving frame formulae. It then covers n + 1 splitting adapted to space slices, constraints and evolution, Hamiltonian and symplectic formulation, Cauchy ... More


Dynamic Models of Investment

Fabio-Cesare Bagliano and Giuseppe Bertola

in Models for Dynamic Macroeconomics

Published in print:
2004
Published Online:
January 2005
ISBN:
9780199266821
eISBN:
9780191601606
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199266824.003.0002
Subject:
Economics and Finance, Macro- and Monetary Economics

Introduces continuous‐time Hamiltonian and stochastic calculus techniques in the presence of convex adjustment costs or irreversibility constraints. Dynamic optimality conditions and phase diagram ... More


QUANTUM DESCRIPTION OF LIGHT-MATTER COUPLING IN SEMICONDUCTORS

Alexey V. Kavokin and Jeremy J. Baumberg

in Microcavities

Published in print:
2007
Published Online:
May 2008
ISBN:
9780199228942
eISBN:
9780191711190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228942.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter starts from description of Rabi and Bloch-oscillations in semiconductors. It introduces the exciton-light coupling Hamiltonian in terms of the secondary quantization theory, and ... More


Introduction to Quantum Theory

Wai-Kee Li, Gong-Du Zhou, and Thomas Chung Wai Mak

in Advanced Structural Inorganic Chemistry

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199216949
eISBN:
9780191711992
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216949.003.0001
Subject:
Physics, Crystallography: Physics

This chapter covers the rudiments of quantum theory, including the dual nature of light and matter, the Uncertainty Principle and probability concept, the electronic wavefunction, and the probability ... More


THE 3+1 FORMALISM

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

There are several different approaches to the problem of separating the Einstein field equations in a way that allows us to give certain initial data, and from there obtain the subsequent evolution ... More


INTRODUCTION

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the introductory Chapter 1 a few representative instances of isochronous dynamical systems are tersely reviewed.


SYSTEMS OF ODEs: MANY-BODY PROBLEMS, NONLINEAR HARMONIC OSCILLATORS

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 4—the longer one in this book—a lemma is first introduced and several isochronous systems of ODEs encompassed by it are treated. One-, two-, three- and multi-dimensional isochronous ... More


Time Evolution

Gary E. Bowman

in Essential Quantum Mechanics

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

The time-dependent Schrödinger equation forms the chapter's starting point. For a time-independent Hamiltonian, a quantum state may be time evolved with the standard, unitary time evolution operator. ... More


The Time-Independent Schrödinger Equation

Gary E. Bowman

in Essential Quantum Mechanics

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

After revisiting the time-dependent Schrödinger equation and introducing the Hamiltonian operator, the time-independent Schrödinger equation (TISE) is obtained. Conditions on acceptable wavefunctions ... More


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