Signature of phase coherence in mesoscopic systems

At low temperature, electronic wave functions in a metal keep their phase coherence on a length Lφ which can be of the order of few microns. Transport and thermodynamic properties of mesoscopic systems whose size are smaller than Lφ 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 difference between: • - Connected open systems, characterized by their transmission properties accessible through conductance measurements. • - Isolated closed systems characterized by their energy level spectra and investigated 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 quantum oscillations of the magneto-conductance on a connected system are indeed only a small fraction of the classical conductance and can much larger on an isolated system.