Quantum point contacts are elementary building blocks of numerous
semiconducting nanodevices. Despite their simple structure, however, their
conductance properties exhibit anomalous features, collectively known as the
"0.7-anomaly", whose origin is still subject to controversial discussions. We
offer a detailed microscopic explanation for the 0.7-anomaly and the zero-bias
peak that typically accompanies it: the common origin of both is a smeared van
Hove singularity in the local density of states at the bottom of the lowest one-
dimensional subband of the point contact, which causes an anomalous
enhancement in the Hartree potential barrier, magnetic spin susceptibility and
inelastic scattering rate. We present theoretical calculations and experimental
results that show good qualitative agreement for the dependence of the
conductance on gate voltage, magnetic field, temperature, source-drain voltage
(including the zero-bias peak) and interaction strength. For low energies we
predict and observe Fermi-liquid behavior analogous to that known for the
Kondo effect in quantum dots. At high energies, however, the analogy between
0.7-anomaly and Kondo effect ceases to be applicable.