A new nonlinear quantum effect in the propagation of a small-amplitude acoustic pulse in metals

Collisionless absorption of short one-dimensional acoustic pulses propagating in metals is considered. The size a of such pulses is much smaller than the electron mean free path, and the characteristic energy U0 of interaction between the sound and electrons is much smaller than the quantum uncertainty E0 = ℏ2/ma2 in the electron energy. It is shown that in view of the one-dimensional nature of electron scattering at a sound packet, the sound absorption coefficient does not tend to a constant in the limit U0 → 0 in some physically important situations, but increases according to the law ln (U0/E0). This anomaly is observed when the dispersion relation of an electron as a function of the electron momentum in the direction of sound propagation has closely spaced extrema separated by energies ⩽ (U0(U0/E0) (coherent magnetic breakdown). A universal expression is obtained from the first principles for the energy absorption in a moving localized perturbation of any origin in terms of the S-matrix of electron scattering. The predicted phenomenon is explained by using analytic properties of the S-matrix.

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