Signature of phase coherence in mesoscopic systems

At low temperature, electronic wave functions in a metal keep their phase c oherence on a length L phi which can be of the order of few microns. Transp ort and thermodynamic properties of mesoscopic systems whose size are small er than L phi exhibit spectacular signatures of this coherence which can be revealed by instance through the sensitivity of the phase of the electrons to an applied vector potential. These quantum effects crucially depend on the way measurements are performed, in this paper we emphasize the differen ce between: - Connected open systems, characterized by their transmission properties ac cessible through conductance measurements. - Isolated closed systems characterized by their energy level spectra and i nvestigated through thermodynamic (mostly magnetization) and ac conductance (response to an electromagnetic wave) measurements. They correspond to different types of coupling to the measuring apparatus, and present different sensitivities to phase coherence. The amplitude of qu antum oscillations of the magnetoconductance on a connected system are inde ed only a small fraction of the classical conductance and can much larger o n an isolated system.