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Quantum Physics in One Dimension

Thierry Giamarchi

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book presents correlated systems in one dimension. Recent progress in nanotechnology and material research has made one-dimensional systems a crucial part of today's physics. After an ... More


COUPLED FERMIONIC CHAINS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines how one-dimensional physics is changed when one goes from a purely one-dimensional system to a two- or three-dimensional situation. Such an effect can be realized by ... More


DISORDERED SYSTEMS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the effects of disorder in fermionic systems, including Anderson localization. There are important differences for the disorder effects between the one-dimensional world, where ... More


SIGNIFICANT OTHERS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter looks at less usual realizations of Luttinger liquids than the ones coming from fermionic systems. The first realization is provided by interacting bosons. Indeed, in one dimension it is ... More


BOSONIZATION

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter explains bosonization, a useful technique for describing the low-energy properties of one-dimensional systems. Bosonization is introduced by presenting a model on which this method is ... More


PECULIARITIES OF D = 1

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter provides an overview of the basic ideas of interacting electrons and the peculiarities of one dimension. Interactions among particles are what endows the one-dimensional world with its ... More


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


METAL–INSULATOR TRANSITIONS

V.F. Gantmakher

in Electrons and Disorder in Solids

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567561
eISBN:
9780191718267
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567561.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

In this chapter, various data on localization in one and three dimensional (1D and 3D) systems are gathered into a unified pattern. Using the Landauer formula, it is shown that random potential ... More


LUTTINGER LIQUIDS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The bosonization technique is useful for solving the interacting problem and for extracting a certain number of properties such as power law behavior of the correlation functions. However, this ... More


INTERACTING FERMIONS ON A LATTICE

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the canonical microscopic models used to study interacting fermions. Most of these models are quite general and are not special to one dimension. These models try to implement ... More


REFINEMENTS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents some additional complications that arise in addition to the simple Luttinger liquid theory for one-dimensional systems. Examples of pitfalls into which the bosonization ... More


BOUNDARIES AND ISOLATED IMPURITIES

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter looks at the effects of individual impurities and boundaries in a Luttinger liquid. Such effects are especially important in Luttinger liquids realized in mesoscopic (or nanoscopic) ... More


MICROSCOPIC METHODS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the various microscopic methods used to tackle one-dimensional systems: the famous Bethe-ansatz and numerical techniques. In addition to the Bethe-ansatz, various numerical ... More


Polaritons: Excitonic States Taking Account of Retardation

Vladimir M. Agranovich

in Excitations in Organic Solids

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents the microscopical theory of polaritons, being coherent superposition of one exciton and one transverse photon state. The dispersion of polaritons including the effect of spatial ... More


Topological superconducting phases in one dimension

Felix von Oppen, Yang Peng, and Falko Pientka

in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

Published in print:
2017
Published Online:
March 2017
ISBN:
9780198785781
eISBN:
9780191827600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198785781.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

These lecture notes give a pedagogical account of the basic physics of Majorana bound states and the topological superconductors that host them. They introduce the basic concepts, as well as possible ... More


Collective effects in quantum systems

Thierry Giamarchi

in Current Trends in Atomic Physics

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198837190
eISBN:
9780191873973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198837190.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics, Particle Physics / Astrophysics / Cosmology

The goal of the course was to introduce the methods allowing to treat quantum systems of interacting particles and discuss the resulting physics. Unfortunately time constraints prevent the author ... More


Real-valued Deterministic Processes

Arno Berger and Theodore P. Hill

in An Introduction to Benford's Law

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691163062
eISBN:
9781400866588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691163062.003.0006
Subject:
Mathematics, Probability / Statistics

In science, one-dimensional deterministic (i.e., non-random) systems provide the simplest models for processes that evolve over time. Mathematically, these models take the form of one-dimensional ... More


Handling the symmetry in 1D compounds

Enric Canadell, Marie-Liesse Doublet, and Christophe Iung

in Orbital Approach to the Electronic Structure of Solids

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199534937
eISBN:
9780191774935
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534937.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

Chapter 3 obtained the mathematical expression for the Bloch orbitals of a periodic system by building a linear combination of orbitals adapted to the translational symmetry of the system. This ... More


Nonequilibrium density matrix for thermal transport in quantum field theory

Benjamin Doyon

in Strongly Interacting Quantum Systems out of Equilibrium: Lecture Notes of the Les Houches Summer School: Volume 99, August 2012

Published in print:
2016
Published Online:
August 2016
ISBN:
9780198768166
eISBN:
9780191821905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198768166.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers one-dimensional quantum systems simultaneously near to, but not exactly at, a critical point and in a far-from-equilibrium steady state. The description uses a density matrix ... More


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