Nonlinear Interaction of Zero Sound with the Order Parameter Collective Modes in Superfluid HELIUM-3-BORON.
A brief overview of past experimental and theoretical investigations of the linear and nonlinear interaction of zero sound with the order parameter collective modes in superfluid ^3He-B is given before introducing the quasiclassical (QC) theory of superfluid ^3He. A new approach to calculating the linear and nonlinear response is presented. The QC propagator is calculated by expanding the low energy Dyson's equation in powers of the nonequilibrium self energy. The expression given for the expansion coefficients, involving products of pairs of equilibrium Green's functions, has a simple diagrammatic representation, and establishes a connection between the QC theory and other theoretical formalisms which have been used to investigate the collective modes. It is shown that the expansion coefficients satisfy Onsager-like relations and some identities required by gauge and galilean invariance. Consequently, this new approach to deriving dynamical equations for the collective modes is more efficient and transparent than solving the QC transport equations. This new approach is used to investigate the linear coupling of zero sound to the order parameter collective modes in weakly inhomogeneous superfluid ^3 He. It makes tractable the treatment of (nonlinear) parametric processes involving zero sound and the collective modes. It is shown that the approximate particle-hole symmetry of the ^3He Fermi liquid determines important selection rules for nonlinear acoustic processes, just as it is well known to do for linear processes. Analogues with nonlinear optics guide the derivation, solution and interpretation of the dynamical equations for a three-wave resonance between two zero sound waves and the J = 2 ^+ order parameter collective mode. It is shown that stimulated Raman scattering and two phonon absorption of zero sound by the J = 2^+ collective mode should be observable when the pump sound wave has energy density larger than about one percent of the superfluid condensation energy density. Generation of anti-Stokes waves and third harmonics should also be observable if the sound path length is small enough to reduce the interference effects of dispersion. Finally, the feasibility of using nonlinear acoustics in ^3He-B to observe quantum mechanical properties of sound is considered.
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- Physics: Fluid and Plasma; Physics: Condensed Matter; Physics: Acoustics