Aspects topologiques de la physique en basse dimension : Les Houches, session LXIX, 7-31 July 1998 = Topological aspects of low dimensional systems

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Aspects topologiques de la physique en basse dimension : Les Houches, session LXIX, 7-31 July 1998 = Topological aspects of low dimensional systems / edited by A. Comtet, T. Jolicœur, S. Ouvry and F. David

資料種別:

図書

出版情報:

Berlin : Springer in cooperation with the NATO Scientific Affair Division
Les Ulis : EDP sciences, 1999

形態:

xxxiv, 909 p. ; 23 cm

著者名:

ISBN:

9783540669098 [3540669094] (: Springer)
9782868834249 [2868834248] (: EDP sciences)

書誌ID:

BA46418538

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書誌詳細

その他の標題:

Topological aspects of low dimensional systems : Les Houches, session LXIX, NATO ASI
École de physique des Houches-UJF & INPG-Grenoble

注記:

At head of title: École de physique des Houches-UJF & INPG-Grenoble
"Les Houches, session LXIX, 7- 31 July 1998 "
"A NATO advanced study institute."
Includes bibliographical references

主題:

Mathematical physics--Congresses; Topology--Congresses

言語:

英語; フランス語

目次情報:

Lecturers

Participants

Préface

Preface

Contents

Electrons in a Flatland / M. ShayeganCourse 1：

Introduction / 1：

Samples and measurements / 2：

2D electrons at the GaAs/AlGaAs interface / 2.1：

Magnetotransport measurement techniques / 2.2：

Ground states of the 2D System in a strong magnetic field / 3：

Shubnikov-de Haas oscillations and the IQHE / 3.1：

FQHE and Wigner crystal / 3.2：

Composite fermions / 4：

Ferromagnetic state at ν = 1 and Skyrmions / 5：

Correlated bilayer electron states / 6：

Overview / 6.1：

Electron System in a wide, single, quantum well / 6.2：

Evolution of the QHE states in a wide quantum well / 6.3：

Evolution of insulating phases / 6.4：

Many-body, bilayer QHE at ν = 1 / 6.5：

Spontaneous interlayer Charge transfer / 6.6：

Summary / 6.7：

The Quantum Hall Effect: Novel Excitations and Broken Symmetries / S.M.GirvinCourse 2：

The quantum Hall effect

Why 2D is important / 1.1：

Constructing the 2DEG / 1.3：

Why is disorder and localization important? / 1.4：

Classical dynamics / 1.5：

Semi-classical approximation / 1.6：

Quantum dynamics in strong B Fields / 1.7：

IQHE edge states / 1.8：

Semiclassical percolation picture / 1.9：

Fractional QHE / 1.10：

The ν = 1 many-body state / 1.11：

Neutral collective excitations / 1.12：

Charged excitations / 1.13：

FQHE edge states / 1.14：

Quantum hall ferromagnets / 1.15：

Coulomb exchange / 1.16：

Spin wave excitations / 1.17：

Effective action / 1.18：

Topological excitations / 1.19：

Skyrmion dynamics / 1.20：

Skyrme lattices / 1.21：

Double-layer quantum Hall ferromagnets / 1.22：

Pseudospin analogy / 1.23：

Experimental background / 1.24：

Interlayer phase coherence / 1.25：

Interlayer tunneling and tilted field effects / 1.26：

Lowest Landau level projection / Appendix A：

Berry's phase and adiabatic transport / Appendix B：

Aspects of Chern-Simons Theory / G.V.DunneCourse 3：

Basics of planar field theory

Chern-Simons coupled to matter fields - "anyons"

Maxwell-Chern-Simons: Topologically massive gauge theory

Fermions in 2 + 1-dimensions / 2.3：

Discrete symmetries: <$>{\cal P}, {\cal C}<$> and <$>{\cal T}<$> / 2.4：

Poincaré algebra in 2 + 1-dimensions / 2.5：

Nonabelian Chern-Simons theories / 2.6：

Canonical quantization of Chern-Simons theories

Canonical structure of Chern-Simons theories

Chern-Simons quantum mechanics

Canonical quantization of abelian Chern-Simons theories / 3.3：

Quantization on the torus and magnetic translations / 3.4：

Canonical quantization of nonabelian Chern-Simons theories / 3.5：

Chern-Simons theories with boundary / 3.6：

Chern-Simons vortices

Abelian-Higgs model and Abrikosov-Nielsen-Olesen vortices / 4.1：

Relativistic Chern-Simons vortices / 4.2：

NonabelianrelativisticChern-Simonsvortices / 4.3：

Nonrelativistic Chern-Simons vortices: Jackiw-Pi model / 4.4：

NonabeliannonrelativisticChern-Simonsvortices / 4.5：

Vortices in the Zhang-Hansson-Kivelson model for FQHE / 4.6：

Vortex dynamics / 4.7：

Induced Chern-Simons terms

Perturbatively induced Chern-Simons terms: Fermion loop / 5.1：

Induced currents and Chern-Simons terms / 5.2：

Induced Chern-Simons terms without fermions / 5.3：

A finite temperature puzzle / 5.4：

Quantum mechanical finite temperature model / 5.5：

Exact finite temperature 2 + 1 effective actions / 5.6：

Finite temperature perturbation theory and Chern-Simons terms / 5.7：

Anyons / J. MyrheimCourse 4：

The concept of particle statistics

Statistical mechanics and the many-body problem

Experimental physics in two dimensions

The algebraic approach: Heisenberg quantization

More general quantizations

The configuration space

The Euclidean relative space for two particles

Dimensions d = 1, 2, 3

Homotopy

The braid group

Schrödinger quantization in one dimension

Heisenberg quantization in one dimension

The coordinate representation

Schrödinger quantization in dimension d ≥ 2

Scalar wave functions

Interchange phases

The statistics vector potential

The N-particle case

Chern-Simons theory

The Feynman path integral for anyons

Eigenstates for Position and momentum

The path integral

Conjugation classes in S_N

The non-interacting case

Duality of Feynman and Schrödinger quantization

The harmonic oscillator / 7：

The two-dimensional harmonic oscillator / 7.1：

Two anyons in a harmonic oscillator potential / 7.2：

More than two anyons / 7.3：

The three-anyon problem / 7.4：

The anyon gas / 8：

The cluster and virial expansions / 8.1：

First and second order perturbative results / 8.2：

Regularization by periodic boundary conditions / 8.3：

Regularization by a harmonic oscillator potential / 8.4：

Bosons and fermions / 8.5：

Two anyons / 8.6：

Three anyons / 8.7：

The Monte Carlo method / 8.8：

The path integral representation of the coefficients <$>G_{\cal P}<$> / 8.9：

Exact and approximate polynomials / 8.10：

The fourth virial coefficient of anyons / 8.11：

Two polynomial theorems / 8.12：

Charged particles in a constant magnetic field / 9：

One particle in a magnetic field / 9.1：

Two anyons in a magnetic field / 9.2：

The anyon gas in a magnetic field / 9.3：

Interchange phases and geometric phases / 10：

Introduction to geometric phases / 10.1：

Two particles in a magnetic field / 10.2：

Interchange of two anyons in potential wells / 10.4：

Laughlin's theory of the fractional quantum Hall effect / 10.5：

Generalized Statistics in One Dimension / A.P. PolychronakosCourse 5：

Permutation group approach

Realization of the reduced Hilbert space

Path integral and generalized statistics

Cluster decomposition and factorizability

One-dimensional systems: Calogero model

The Calogero-Sutherland-Moser model

Large-N properties of the CSM model and duality

One-dimensional systems: Matrix model

Hermitian matrix model

The unitary matrix model

Quantization and spectrum

Reduction to spin-particle systems

Operator approaches

Exchange operator formalism

Systems with internal degrees of freedom

Asymptotic Bethe ansatz approach

The freezing trick and spin models

Exclusion statistics

Motivation from the CSM model

Semiclassics - Heuristics

Exclusion statistical mechanics

Exclusion statistics path integral

Is this the only "exclusion" statistics?

Epilogue

Lectures on Non-perturbative Field Theory and Quantum Impurity Problems / H.SaleurCourse 6：

Some notions of conformal field theory

The free boson via path integrals

Normal ordering and OPE

The stress energy tensor

Conformal in(co)variance

Some remarks on Ward identities in QFT

The Virasoro algebra: Intuitive introduction

Cylinders

The free boson via Hamiltonians

Modular invariance

Conformal invariance analysis of quantum impurity fixed points

Boundary conformal field theory

Partition functions and boundary states

Boundary entropy

The boundary sine-Gordon model: General results

The model and the flow

Perturbation near the UV fixed point

Perturbation near the IR fixed point

An alternative to the instanton expansion: The conformal invariance analysis

Search for integrability: Classical analysis

Quantum integrability

Conformal perturbation theory

S-matrices

Back to the boundary sine-Gordon model

The thermodynamic Bethe-ansatz: The gas of particles with "Yang-Baxter statistics"

Zamolodchikov Fateev algebra

The TBA

A Standard computation: The central Charge

Thermodynamics of the flow between N and D fixed points

Using the TBA to compute static transport properties

Tunneling in the FQHE

Conductance without impurity

Conductance with impurity

Quantum Partition Noise and the Detection of Fractionally Charged Laughlin Quasiparticles / D.C. GlattliSeminar 1：

Partition noise in quantum conductors

Quantum partition noise

Partition noise and quantum statistics

Quantum conductors reach the partition noise limit

Experimental evidences of quantum partition noise in quantum conductors

Partition noise in the quantum Hall regime and determination of the fractional Charge

Edge states in the integer quantum Hall effect regime

Tunneling between IQHE edge channels and partition noise

Edge channels in the fractional regime

Noise predictions in the fractional regime

Measurement of the fractional Charge using noise

Beyond the Poissonian noise of fractional charges

Mott Insulators, Spin Liquids and Quantum Disordered Superconductivity / Matthew P.A. FisherCourse 7：

Models and metals

Noninteracting electrons

Interaction effects

Mott insulators and quantum magnetism

Spin models and quantum magnetism

Spin liquids

Bosonization primer

2 Leg Hubbard ladder

Bonding and antibonding bands

Interactions

Bosonization

d-Mott phase

Symmetry and doping

d-Wave superconductivity

BGS theory re-visited

d-wave symmetry

Continuum description of gapless quasiparticles

Effective field theory

Quasiparticles and phase flucutations

Nodons

Vortices

ic/2e versus hc/e vortices

Duality

Nodal liquid phase

Half-filling

Doping the nodal liquid

Closing remarks

Lattice duality

Two dimensions / A.1：

Three dimensions / A.2：

Statistics of Knots and Entangled Random Walks / S. NechaevCourse 8：

Lecturers

Participants

Préface

Preface

Contents

Electrons in a Flatland / M. ShayeganCourse 1：

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