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We study the relationship between the local density of states (LDOS) and theconductance variation $\Delta G$ in scanning-gate-microscopy experiments onmesoscopic structures as a charged tip scans above the sample surface. Wepresent an analytical model showing that in the linear-response regime theconductance shift $\Delta G$ is proportional to the Hilbert transform of theLDOS and hence a generalized Kramers-Kronig relation holds between LDOS and$\Delta G$. We analyze the physical conditions for the validity of thisrelationship both for one-dimensional and two-dimensional systems when severalchannels contribute to the transport. We focus on realistic Aharonov-Bohm ringsincluding a random distribution of impurities and analyze the LDOS-$\Delta G$correspondence by means of exact numerical simulations, when localized statesor semi-classical orbits characterize the wavefunction of the system.

Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy