## Low-Dimensional Systems: Interactions and Transport PropertiesExperimental progress over the past few years has made it possible to test a n- ber of fundamental physical concepts related to the motion of electrons in low dimensions. The production and experimental control of novel structures with typical sizes in the sub-micrometer regime has now become possible. In parti- lar, semiconductors are widely used in order to con?ne the motion of electrons in two-dimensional heterostructures. The quantum Hall e?ect was one of the ?rst highlights of the new physics that is revealed by this con?nement. In a further step of the technological development in semiconductor-heterostructures, other arti?cial devices such as quasi one-dimensional ‘quantum wires’ and ‘quantum dots’ (arti?cial atoms) have also been produced. These structures again di?er very markedly from three- and two-dimensional systems, especially in relation to the transport of electrons and the interaction with light. Although the technol- ical advances and the experimental skills connected with these new structures are progressing extremely fast, our theoretical understanding of the physical e?ects (such as the quantum Hall e?ect) is still at a very rudimentary level. In low-dimensional structures, the interaction of electrons with one another and with other degrees of freedoms such as lattice vibrations or light gives rise to new phenomena that are very di?erent from those familiar in the bulk ma- rial. The theoretical formulation of the electronic transport properties of small devices may be considered well-established, provided interaction processes are neglected. |

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### Contents

Nonequilibrium Mesoscopic Conductors Driven by Reservoirs | 3 |

A Linear Response Theory of 1DElectron Transport Based on Landauer Type Model | 23 |

Gapped Phases of Quantum Wires | 37 |

Interaction Effects in OneDimensional Semiconductor Systems | 79 |

Correlated Electrons in Carbon Nanotubes | 96 |

Bosonization Theory of the Resonant Raman Spectra of Quantum Wires | 113 |

An Introduction to RealTime Renormalization Group | 134 |

Spin States and Tkansport in Correlated Electron Systems | 167 |

Nonlinear Transport in QuantumHall Smectics | 195 |

Thermodynamics of Quantum Hall Ferromagnets | 207 |

### Other editions - View all

Low-Dimensional Systems: Interactions and Transport Properties Tobias Brandes No preview available - 2000 |

### Common terms and phrases

1D channel 1D system amplitudes approximation backscattering band behavior bosonic calculate charge chemical potential conductance consider contribution Cooper phase Correlated Electron Systems correlation function corresponds Coulomb interaction coupling cutoff deﬁned denotes density matrix described diagram effect electron correlation energy excitations Fermi liquid Fermi velocity fermionic ferromagnetic filling factor ﬁnd ﬁnite ﬁrst ﬂuctuations gapless Green’s function Hamiltonian Hartree-Fock Hubbard model impurity scattering integral inter-subband interacting electrons interband kernel Kubo formula Landau level lattice Lett linear Luttinger liquid magnetic ﬁeld matrix elements mesoscopic modes nanotubes nonequilibrium steady obtained operators parameters particle Phys physics power-law propagator properties quantum dots quantum Hall quantum wires Raman renormalization group repulsive reservoirs resonance result RG equations semiconductor stripes subbands superconducting SWNTs temperature dependence theory Tomonaga-Luttinger transport tunneling vertex vertices wave number wavefunction