  We present a theoretical approach for understanding the stability of simple
metal nanowires, in particular monovalent metals such as the alkalis and noble
metals. Their cross sections are of order one nanometer so that small
perturbations from external (usually thermal) noise can cause large geometrical
deformations. The nanowire lifetime is defined as the time required for making
a transition into a state with a different cross-sectional geometry. This can
be a simple overall change in radius, or a change in the cross section shape,
or both. We develop a stochastic field theoretical model to describe this
noise-induced transition process, in which the initial and final states
correspond to locally stable states on a potential surface derived by solving
the Schrodinger equation for the electronic structure of the nanowire
numerically. The numerical string method is implemented to determine the
optimal transition path governing the lifetime. Using these results, we
tabulate the lifetimes of sodium and gold nanowires for several different
initial geometries.
