Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects

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.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure

Schwinger's Dynamical Casimir Effect: Bulk Energy Contribution

Schwinger's Dynamical Casimir Effect is one of several candidate explanations for sonoluminescence. Recently, several papers have claimed that Schwinger's estimate of the Casimir energy involved is grossly inaccurate. In this letter, we show that these calculations omit the crucial volume term. When the missing term is correctly included one finds full agreement with Schwinger's result for the Dynamical Casimir Effect. We have nothing new to say about sonoluminescence itself except to affirm that the Casimir effect is energetically adequate as a candidate explanation.Comment: 6 pages. Uses LaTeX with RevTeX package in two-column forma

Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of photon production due to changes in the properties of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric bubble. This mechanism can be re-phrased in terms of the Casimir effect and has recently been the subject of considerable controversy. The present paper probes Schwinger's suggestion in detail: Using the sudden approximation we calculate Bogolubov coefficients relating the QED vacuum in the presence of the expanded bubble to that in the presence of the collapsed bubble. In this way we derive an estimate for the spectrum and total energy emitted. We verify that in the sudden approximation there is an efficient production of photons, and further that the main contribution to this dynamic Casimir effect comes from a volume term, as per Schwinger's original calculation. However, we also demonstrate that the timescales required to implement Schwinger's original suggestion are not physically relevant to sonoluminescence. Although Schwinger was correct in his assertion that changes in the zero-point energy lead to photon production, nevertheless his original model is not appropriate for sonoluminescence. In other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/9905034) we have developed a variant of Schwinger's model that is compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is now limited to providing a probe of Schwinger's original suggestion for sonoluminescence. For details on our own variant of Schwinger's ideas see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503

A modified Schwinger's formula for the Casimir effect

After briefly reviewing how the (proper-time) Schwinger's formula works for computing the Casimir energy in the case of "scalar electrodynamics" where the boundary conditions are dictated by two perfectly conducting parallel plates with separation "a" in the Z-axis, we propose a slightly modification in the previous approach based on an analytical continuation method. As we will see, for the case at hand our formula does not need the use of Poisson summation to get a (renormalized) finite result.Comment: 6 pages, DFTUZ/93/14 (a short version will appear in the Letters in Math. Phys.

Magnetic Permeability of Constrained Fermionic Vacuum

We obtain using Schwinger's proper time approach the Casimir-Euler-Heisenberg effective action of fermion fluctuations for the case of an applied magnetic field. We implement here the compactification of one space dimension into a circle through anti-periodic boundary condition. Aside of higher order non-linear field effects we identify a novel contribution to the vacuum permeability. These contributions are exceedingly small for normal electromagnetism due to the smallness of the electron Compton wavelength compared to the size of the compactified dimension, if we take the latter as the typical size of laboratory cavities, but their presence is thought provoking, also considering the context of strong interactions.Comment: 8 pages, LaTex, 1 postscript figure, Phys. Let. B in press, slight text revisions, references adde

THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL

Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds for every instanton sector. This is due to Theta-invariance of the Schwinger model.Comment: LATEX file 11 pages, no figure

Sonoluminescence as a QED vacuum effect. I: The Physical Scenario

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of changes in the properties of the quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased in terms of changes in the Casimir Energy: changes in the distribution of zero-point energies and has recently been the subject of considerable controversy. The present paper further develops this quantum-vacuum approach to sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum states in the presence of a homogeneous medium of changing dielectric constant. In this way we derive an estimate for the spectrum, number of photons, and total energy emitted. We emphasize the importance of rapid spatio-temporal changes in refractive indices, and the delicate sensitivity of the emitted radiation to the precise dependence of the refractive index as a function of wavenumber, pressure, temperature, and noble gas admixture. Although the physics of the dynamical Casimir effect is a universal phenomenon of QED, specific experimental features are encoded in the condensed matter physics controlling the details of the refractive index. This calculation places rather tight constraints on the possibility of using the dynamical Casimir effect as an explanation for sonoluminescence, and we are hopeful that this scenario will soon be amenable to direct experimental probes. In a companion paper we discuss the technical complications due to finite-size effects, but for reasons of clarity in this paper we confine attention to bulk effects.Comment: 25 pages, LaTeX 209, ReV-TeX 3.2, eight figures. Minor revisions: Typos fixed, references updated, minor changes in numerical estimates, minor changes in some figure

Decay widths and scattering processes in massive QED2_2

Using mass perturbation theory, we infer the bound-state spectrum of massive QED$_2$ and compute some decay widths of unstable bound states. Further, we discuss scattering processes, where all the resonances and particle production thresholds are properly taken into account by our methods.Comment: Latex file, 5 pages, 8 ps-figures & 1 style-file; written version of a talk given at the QCD97 conference in Montpellier, Franc

Boundary conditions in local electrostatics algorithms

We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We firstly show how to implement constant-potential, Dirichlet, boundary conditions by introducing extra Monte Carlo moves to the algorithm. Secondly, we show the interest of the algorithm for studying systems which require anisotropic electrostatic boundary conditions for simulating planar geometries such as membranes.Comment: 8 pages, 6 figures, accepted in JC

Quantum radiation in external background fields

A canonical formalism is presented which allows for investigations of quantum radiation induced by localized, smooth disturbances of classical background fields by means of a perturbation theory approach. For massless, non-selfinteracting quantum fields at zero temperature we demonstrate that the low-energy part of the spectrum of created particles exhibits a non-thermal character. Applied to QED in varying dielectrics the response theory approach facilitates to study two distinct processes contributing to the production of photons: the squeezing effect due to space-time varying properties of the medium and of the velocity effect due to its motion. The generalization of this approach to finite temperatures as well as the relation to sonoluminescence is indicated.Comment: 20 page