Energy Dissipation Mechanism for Quantum Mechanical Tunneling in Viscoelastic Relaxation

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Abstract
Inelastic tunneling is proposed as a viscoelastic relaxation mechanism at low temperatures for polymers possessing methyl groups capable of rotation. In the process of dynamic mechanical excitation of the sample, the heights of the barriers which restrict the rotation of methyl groups are modulated periodically at the external excitation frequency. The change in the over‐all barrier height is accompanied simultaneously by a change in the torsional energy levels of the methyl rotors. If rotational tunneling occurs between the same torsional states but differing slightly in energy (the difference in energy being due solely to the modulation of the barrier height by the stress field), then the difference in energy is given off as a phonon. Since tunneling is a random process, the phonons thus emitted are not coherent with the external excitation, and by interaction with the phonon bath of the sample they are thermalized, i.e., their energy is converted into heat. The concept of inelastic tunneling is reviewed briefly and the coupling of the rotational tunneling process to the phonon field is discussed, as are also the energetics of the process.