  We review data analysis techniques that can be used to study temporal
correlations among conductance traces in break junction measurements. We show
that temporal histograms are a simple but efficient tool to check the temporal
homogeneity of the conductance traces, or to follow spontaneous or triggered
temporal variations, like structural modifications in trained contacts, or the
emergence of single-molecule signatures after molecule dosing. To statistically
analyze the presence and the decay time of temporal correlations, we introduce
shifted correlation plots. Finally, we demonstrate that correlations between
opening and subsequent closing traces may indicate structural memory effects in
atomic-sized metallic and molecular junctions. Applying these methods on
measured and simulated gold metallic contacts as a test system, we show that
the surface diffusion induced flattening of the broken junctions helps to
produce statistically independent conductance traces at room temperature,
whereas at low temperature repeating tendencies are observed as long as the
contacts are not closed to sufficiently high conductance setpoints. Applying
opening-closing correlation analysis on Pt-CO-Pt single-molecule junctions, we
demonstrate pronounced contact memory effects and recovery of the molecule for
junctions breaking before atomic chains are formed. However, if chains are
pulled the random relaxation of the chain and molecule after rupture prevents
opening-closing correlations.
