Sonoluminescence as a QED vacuum effect. II. Finite volume effects

Abstract

In a companion paper [quant-ph/9904013] we have investigated several variations of Schwinger's proposed mechanism for sonoluminescence. We demonstrated that any realistic version of Schwinger's mechanism must depend on extremely rapid (femtosecond) changes in refractive index, and discussed ways in which this might be physically plausible. To keep that discussion tractable, the technical computations in that paper were limited to the case of a homogeneous dielectric medium. In this paper we investigate the additional complications introduced by finite-volume effects. The basic physical scenario remains the same, but we now deal with finite spherical bubbles, and so must decompose the electromagnetic field into Spherical Harmonics and Bessel functions. We demonstrate how to set up the formalism for calculating Bogolubov coefficients in the sudden approximation, and show that we qualitatively retain the results previously obtained using the homogeneous-dielectric (infinite volume) approximation.

Sonoluminescence as a QED vacuum effect. I. The physical scenario

“…These result should be be compared with that obtained in the companion paper [38], where we first include finite volume effects and then consider the large-volume limit for dielectric bubbles in order to reproduce the original Schwinger estimate of photon production [9][10][11][12][13][14][15]. It should also be compared with the discussion of Yablonovitch [30] [see particularly the formulae in the paragraph between equations (8) and (9)].…”

“…With this aim in mind we studied the effect of a changing dielectric constant in a homogeneous medium. At this stage of development, we are not concerned with the detailed dynamics of the bubble surface, and confine attention to the bulk effects, deferring consideration of finite-volume effects to the companion paper [38]. 7 It should be noted that similar unphysical features also affect the "shock wave"-based models [1]: Indeed, the Mach number of the shock formally diverges as the shock implodes towards the origin (cf.…”

“…9 In view of this femtosecond change of refractive index, we would be justified in making the sudden approximation for frequencies less than about a PHz. In this paper we do not make this approximation except when convenient in obtaining crude analytic estimates, but when we turn to dealing with finite-size effects in the companion paper [38] the sudden approximation will be more than just a convenience: it will be absolutely essential in keeping the mathematical features of the analysis tractable.…”

Sonoluminescence: two-photon correlations as a test of thermality

“…If the "thermality" in the sonoluminescence spectrum is of this squeezed-mode type, we will ultimately desire a much more detailed model of the dynamical Casimir effect involving an interaction term that produces pairs of photons in two-mode squeezed-states. Apart from our model [15] and its finite volume generalization [16], the Eberlein model also possesses this property [17]. For this type of squeezed-mode photon pair-production in a linear medium with spacetime-dependent dielectric permittivity and magnetic permeability see [18]; for nonlinearity effects see [19].…”

“…These correlations could be measured, for example, by back-to-back symmetrically placed detectors working in coincidence. Finite-size effects have been shown in [16] to perturb only slightly this back-to-back character of the emitted photons, in the sense that back-to-back emission remains largely dominant. (Additionally it has been verified that the form of the spectrum is not violently affected.)…”