Ballistic conductance fluctuation and quantum chaos in sinai billiard

We investigate classical dynamics and quantum transport in weakly-opened square and Sinai billiards in the perpendicular magnetic field B. In the case of square billiard, the correlation field B-c of smoothed conductance varies irregularly with respect to B, while in the case of Sinai billiard it decreases monotonically with increase of B. By comparing between B-c and Lyapunov exponents in wide magnetic field regions, it follows that fluctuation features of B-c are attributed to the stability and instability of phase space in the underlying classical dynamics. In Sinai billiard case, geometry of the billiard yields Aharonov-Bohm oscillation in non-smoothed conductance, suppressing a symptom of chaos. Nevertheless, B-c evaluated in terms of the smoothed conductance nicely mimics the scaled variance of Lyapunov exponents.