Fundamental Aspects of Electron Correlations and Quantum Transport in One-dimensional Systems

Some aspects of physics on interacting fermions in 1D are discussed in a tutoriallike manner. We begin by showing that the non-analytic corrections to the Fermiliquid forms of thermodynamic quantities result from essentially 1D collisions embedded into a higher-dimensional phase space. The role of these collisions increases progressively as dimensionality is reduced until, finally, they lead to a breakdown of the Fermi liquid in 1D. An exact solution of the Tomonaga-Luttinger model, based on the Ward identities, is reviewed in the fermionic language. Tunneling in a 1D interacting systems is discussed first in terms of the scattering theory for interacting fermions and then via bosonization. Universality of conductance quantization in disorder-free quantum wires is discussed along with the breakdown of this universality in the spin-incoherent case. A difference between charge (universal) and thermal (non-universal) conductances is explained in terms of Fabry-Perrot resonances of charge plasmons. Fundamental aspects of electron correlations and quantum transport 5