We consider a system of one-dimensional non-interacting fermions in external harmonic confinement. Using an efficient Green’s function method we evaluate the exact profiles and the pair correlation function, showing a direct signature of the Fermi statistics and of the single quantum-level occupancy. We also study the dynamical properties of the gas, obtaining the spectrum both in the collision...

The path integral quantum-statistical approach to study the magnetic properties of the weakly relativistic interacting electron gas in the inhomogeneous magnetic eld is suggested. In the random phase approximation the thermodynamic potential is calculated. In the case of absolute zero the magnetization and nonlinear magnetic susceptibility of the system are found. Both Landau diamagnetism and P...

We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the scaling ansatz for purely one-dimensional fermion systems and its extension when interchain coupling and dimensionality crossovers are present at finite temperatu...

We analyze the charge transport between a one-dimensional weakly interacting electron gas and a superconductor within the scaling approach in the basis of scattering states. We derive the renormalization group equations, which fully account for the intrinsic energy dependence due to Andreev reflection. A strong renormalization of the corresponding reflection phase is predicted even for a perfec...

The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is reexamined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of the disordered system are shown to be current carrying, with exactly the same Hall current as in the absence of disorder. There are no localized states. Acco...

The photon-absorption edge in a weakly interacting one-dimensional electron gas is studied, treating backscattering of conduction electrons from the core hole exactly. Close to threshold, there is a power-law singularity in the absorption, I(ǫ) ∝ ǫ−α, with α = 3/8 + δ+/π − δ2 +/2π where δ+ is the forward scattering phase shift of the core hole. In contrast to previous theories, α is finite (and...

The two-dimensional electron gas at the interface between LaAlO(3) and SrTiO(3) has become one of the most fascinating and highly debated oxide systems of recent times. Here we propose that a one-dimensional electron gas can be engineered at the step edges of the LaAlO(3)/SrTiO(3) interface. These predictions are supported by first-principles calculations and electrostatic modeling which elucid...

We establish the consistency of the Fermi liquid description and find a relation between the Fermi liquid constants for a two-dimensional electron system near the point of full polarization due to a parallel magnetic field H. Our results enable us to predict connections between different thermodynamic properties of the system. In particular, we find that near the point of full polarization Hc ,...