  A remarkably quantitative understanding of the electrical and mechanical
properties of metal wires with a thickness on the scale of a nanometer has been
obtained within the free-electron model using semiclassical techniques.
Convergent trace formulas for the density of states and cohesive force of a
narrow constriction in an electron gas, whose classical motion is either
chaotic or integrable, are derived. Mode quantization in a metallic point
contact or nanowire leads to universal oscillations in its cohesive force,
whose amplitude depends only on a dimensionless quantum parameter describing
the crossover from chaotic to integrable motion, and is of order 1nN, in
agreement with experiments on gold nanowires. A linear stability analysis shows
that the classical instability of a long wire under surface tension can be
completely suppressed by quantum effects, leading to stable cylindrical
configurations whose electrical conductance is a magic number 1, 3, 5, 6,...
times the conductance quantum, in accord with recent results on alkali metal
nanowires.
