We investigate the effect of electron-electron interaction on the temperature dependence of the Hall coefficient of 2D electron gas at arbitrary relation between the temperature T and the elastic mean-free time τ . At small temperature T τ ≪h we reproduce the known relation between the logarithmic temperature dependences of the Hall coefficient and of the longitudinal conductivity. At higher temperatures, this relation is violated quite rapidly; correction to the Hall coefficient becomes ∝ 1/T whereas the longitudinal conductivity becomes linear in temperature.

The "Which Path?" interferometer consists of an Aharonov-Bohm ring with a quantum dot (QD) built in one of its arms, and an additional quantum point contact (QPC) located close to the QD. The transmission coefficient of the QPC depends on the charge state of the QD. Hence the point contact causes controllable dephasing of transport through the QD, and acts as a measurement device for which path an electron takes through the ring. We calculate the suppression of the Aharonov-Bohm oscillations which is caused both by dephasing and by the orthogonality catastrophe, i.e., respectively, by real and virtual electron-hole pair creation at the QPC.

We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors ν ≫ 1. Assuming that the interaction is sufficiently weak, r s < 1, we integrate out all the fast degrees of freedom, and derive the effective Hamiltonian acting in the Fock space of the partially filled Landau level only. This theory enables us to find two energy scales controlling the electron dynamics at energies less thanhω c . The first energy scale, (hω c /ν) ln (νr s ), appears in the one electron spectral density as the width of a pseudogap. The second scale, r sh ω c , is parametrically larger; it characterizes the exchange-enhanced spin splitting and the thermodynamic density of states.

For the first time, we study the tunneling density of states (DOS) of the interacting electron gas beyond the diffusive limit. A strong correction to the DOS persists even at electron energies exceeding the inverse transport relaxation time, which could not be expected from the well-known Altshuler-Aronov-Lee (AAL) theory. This correction originates from the interference between the electron waves scattered by an impurity and by the Friedel oscillation this impurity creates. Account for such processes also revises the AAL formula for the DOS in the diffusive limit.