Phonon description and the Euler buckling instability of a mesoscopic bar at fixed strain

The quantum theory of a mesoscopic beam subjected to fixed compressional strain is discussed from the perspective of phonons and other excitations that emerge from the buckling instability. It is argued that despite the anharmonicity inherent in this instability, elementary excitations maintain their integrity because (i) modes higher than the fundamental remain harmonic through the instability, and (ii) the quantum vibrational frequency of the fundamental, (E-1 - E-o)/h, does not vanish. It is determined by a Landau-like effective potential which is quartic at critical strain. Beyond the buckling instability, phonons recover their harmonic character while a distinct form of excitation evolves associated with the broken symmetry. For a beam of rectangular cross-section these are tunneling modes; for a tube of circular cross-section they are rotational. (C) 2002 Elsevier Science B.V. All rights reserved.