L\'{e}vy flights in quantum transport in quasi-ballistic wires

Conductance fluctuations, localization and statistics of Lyapunov exponents are studied numerically in pure metallic wires with rough boundaries (quasi-ballistic wires). We find that the correlation energy of conductance fluctuations scales anomalously with the sample dimensions, indicating the role of L\'{e}vy flights. Application of a magnetic field deflects the L\'{e}vy flights which reduces the localization length. This deflection also breaks the geometrical flux cancellation and restores the usual Aharonov-Bohm type magneto-conductance fluctuations.