Abstract:
Recent experiments involving semiconducting quantum dots embedded in Aharonov-Bohm interferometry setups suggest that information concerning the phase of electron wavefunctions can be obtained from transport measurements. Here we review the basics of the theory of electron interferometry, some of the relevant experimental results, and recent theoretical developments attempting to shed light on the outstanding dilemmas.

Abstract:
The scattering phase shift of an electron transferred through a quantum dot is studied within a model Hamiltonian, accounting for both the electron--electron interaction in the dot and a finite temperature. It is shown that, unlike in an independent electron picture, this phase may exhibit a phase lapse of $ \pi $ {\em between } consecutive resonances under generic circumstances.

Abstract:
We analyze the average of weak values over statistical ensembles of pre- and post-selected states. The protocol of weak values, proposed by Aharonov et al., is the result of a weak measurement conditional on the outcome of a subsequent strong (projective) measurement. Weak values can be beyond the range of eigenvalues of the measured observable and, in general, can be complex numbers. We show that averaging over ensembles of pre- and post-selected states reduces the weak value within the range of eigenvalues of the measured operator. We further show that the averaged result expressed in terms of pre- and post-selected density matrices, allows us to include the effect of decoherence.

Abstract:
We study the conductance (g) distribution function of an ensemble of isolated conducting rings, with an Aharonov--Bohm flux. This is done in the discrete spectrum limit, i.e., when the inelastic rate, frequency and temperature are all smaller than the mean level spacing. Over a wide range of g the distribution function exhibits universal behavior P(g)\sim g^{-(4+\beta)/3}, where \beta=1 (2) for systems with (without) a time reversal symmetry. The nonuniversal large g tail of this distribution determines the values of high moments.

Abstract:
We have demonstrated that Phi_0 periodic Aharonov--Bohm oscillations measured in a ensemble of rings may survive after ensemble averaging procedure. The central point is the difference between the preparation stage of the ensemble and the subsequent measurement stage. The robustness of the effect under finite temperature and non--zero charging energy of rings is discussed.

Abstract:
A microscopic theory of zero wavelength (q=0) interaction in finite--size systems is proposed. Its exact solution interpolates between the Coulomb blockade and the perturbative Altshuler--Aronov theory, in the strong and weak interaction limits respectively. The tunneling density of states and the quasiparticle life--time are calculated. The physical nature of the q=0 component of the interaction is discussed.

Abstract:
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to spectral correlations in those systems. They are fairly robust and are suppressed at temperatures much higher than the level spacing.

Abstract:
The small energy anomaly in the single particle density of states of disordered interacting systems is studied for the zero dimensional case. This anomaly interpolates between the non--perturbative Coulomb blockade and the perturbative limit, the latter being an extension of the Altshuler--Aronov zero bias anomaly at d=0. Coupling of the zero dimensional system to a dissipative environment leads to an effective screening of the interaction and a modification of the density of states.

Abstract:
Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles due to both quenched disorder and thermodynamical effects. We show how these differences are related to spectral correlations of the system at hand, and evaluate the conditions (temperature, system's size) when the thermodynamic limit is achieved. We demonstrate our approach by evaluating the heat capacity, persistent currents and the occupation probability of single electron states, employing a systematic diagrammatic approach.

Abstract:
We consider a multiple tunneling process into a quantum dot capacitively coupled to a dissipative environment. The problem is mapped onto an anisotropic Kondo model in its Coulomb gas representation. The tunneling barrier resistance and the dissipative resistance of the environment correspond to the transverse and the longitudinal Kondo couplings respectively. We thus identify a line in the parameter space of the problem which corresponds to a zero-temperature Berezinskii-Kosterlitz-Thouless like phase transition. The physics of coupling to the environment is elucidated and experimental consequences of the predicted transition are discussed.