Logarithmic divergence of normal state resistivity of bipolaronic high-Tc cuprates

The resonance Wigner scattering of charged bosons (small bipolarons) in a random potential leads to logarithmically divergent low-temperature resistivity as observed in several cuprates. Unusual temperature dependence of resistivity of $La_{2-x}Sr_{x}CuO_{4}$ as well as of the Hall effect is quantitatively described in a wide temperature range providing an evidence for $2e$ charged Bose-liquid in high-$T_{c}$ cuprates.