## 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