High-energy phonon creation from cold phonons in pulses of different length in He II

Abstract

We have carried out a theoretical investigation of the experimentally observed phenomenon that long-lived high-energy ͑h͒ phonons are generated by a moving cloud of low-energy ͑l͒ phonons. The h phonons are created from the l phonons by four phonon processes (4pp) and they are lost from the trailing edge of the l phonon cloud, because they have a lower velocity than the l phonons, and form the h phonon cloud. We obtain a set of equations which completely describe these phenomenon. The solution of these equations accounts for the high efficiency of the conversion process: a major part of the energy in the l phonons can be converted to h phonons within the propagation time of the pulse (Ͻ10 Ϫ4 s). In short pulses (Ͻ10 Ϫ7 s) the h phonons escape as soon they are created, but in long pulses the h phonon density increases within the l cloud. It is shown that in long phonon pulses there can be a suprathermal number of h phonons within the l cloud. The theory describes the cooling of pulses of different length due to energy being transformed into h phonons. It also accounts well for the important characteristics of h phonon generation which is an unusual example of energy transferring from low-energy to high-energy states.

Interactions between Sheets of Phonons in LiquidHe4

“…It was proposed [6,7], that the phonons in the This shows the bolometer signals for the two separate pulses, dashed-dot lines, and for the double pulse, solid line. the sharp peak at 40 µs is due to the l-phonons and the signal after ≈ 43µs is due to h-phonons.…”

“…However it was recognised that phonons could spontaneously decay by the three phonon process (3pp) [2,3], which is allowed by the upward curvature of the dispersion curve [4,5]. This picture was challenged recently by Adamenko et al [6,7] who argued that a number of observations, such as the creation of high energy phonons in the liquid, could be explained if the phonons in the pulse were treated as strongly interacting and were confined to a narrow cone in momentum space. This has prompted us to look for evidence of the proposed phonon momentum distribution.…”

Three-phonon relaxation in isotropic and anisotropic phonon systems of liquid helium at different pressures

“…1) were studied and analytical expressions (13)- (19) for the boundaries of regions in which three-phonon processes are allowed by the conservation laws of energy and momentum were obtained. The dependence (25) on the angle q p p ¢ ¢¢ between phonons with momenta p¢ and ¢¢ p created as a result of the decay of a phonon with momentum p, using different relations between the momenta of the created phonons, was obtained. This dependence is represented on Fig.…”

“…2 (25). Here q p p ¢ ¢¢ max is the maximum angle between the momenta of the phonons participating in the three-phonon process, which is defined by Eq.…”

“…The approximation (52) has allowed the successful solution of a number of problems [20,[25][26][27][28].…”