  We investigate quantum effects in the mechanical properties of elastic beams
on the nanoscale. Transverse quantum and thermal fluctuations and the nonlinear
excitation energies are calculated for beams compressed in longitudinal
direction. Near the Euler instability, the system is described by a one
dimensional Ginzburg-Landau model where the order parameter is the amplitude of
the buckling mode. We show that in single wall carbon nanotubes with lengths of
order or smaller than 100 nm zero point fluctuations are accessible and discuss
the possibility of observing macroscopic quantum coherence in nanobeams near
the critical strain.
