PHONON-PHONON INTERACTIONS IN BOSE SYSTEMS

Journal Article · Wed Aug 15 04:00:00 EDT 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.127.979· OSTI ID:4775548

Nelkin, M

The stability of phonons in Bose systems is considered. It is noted that the phonons in helium II are stable against decay into two or more phonons, in contrast to the lowdensity Bose gas where the lifetime for decay of onc phonon into two is finite and has been calculated by several authors. The conseqnences of phonon stability for allowable mechanisms of phonon-phonon interaction are considered. It is concluded that virtual three phonon processes may still occur although energy-conserving three-phonon processes cannot take place. The inclusion of such virtual proccsses makes it plausible that the interactions between excitations can be weak, even though the linewidths measured in neutron scattering are larger than the line shifts. The quantum hydrodynamics of Landau and Khalatnikov including nonlinis theory the stability of the phonons is indeterminate and must be legislated. If the phonons are assumed unstable against decay, the phonon lifetime in the low-density and long-wavelength limit can be calculated, and is in agree ment with the results for the atomic theory of the lowdensity Bose gas. This lends considerable plausibility to the quantitative validilty of the Landau-Khalatnikov calculation of phonon-phonon scattering in helium II via an almost energy-conserving intermediate one-phonon state. The paper concludes by comparing the results of an idealized neutron scattering experiment as calculated from the Feynman-Cohen point of view, and from the point of view of the theory of the low-density Bose gas. (auth)

• Research Organization: General Atomic Div., General Dynamics Corp., San Diego, Calif.
• NSA Number: NSA-16-029562
• OSTI ID: 4775548
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 127; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOSE-EINSTEIN GAS
BOSONS
DECAY
DENSITY
ENERGY
EXCITATION
FLUID FLOW
GASES
HELIUM
HYDRODYNAMICS
INTERACTIONS
LIFETIME
NEUTRONS
NUMERICALS
PHONONS
PHYSICS
QUANTUM MECHANICS
SCATTERING
SOUND
SPECTRAL SHIFT
STABILITY