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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

## 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

## 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

## 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

## 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

## 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

## One-dimensional Systems

*Giuseppe Mussardo*

### in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

- Published in print:
- 2020
- Published Online:
- May 2020
- ISBN:
- 9780198788102
- eISBN:
- 9780191830082
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788102.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 2 discusses one-dimensional statistical models, for example, the Ising model and its generalizations (Potts model, systems with O(n) or Zn-symmetry, etc.). It discusses several methods of ... 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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