Sonoluminescence: Bogolubov coefficients for the QED vacuum of a time-dependent dielectric bubble

We extend Schwinger's ideas regarding sonoluminescence by explicitly calculating the Bogolubov coefficients relating the QED vacuum states associated with changes in a dielectric bubble. Sudden (non-adiabatic) changes in the refractive index lead to an efficient production of real photons with a broadband spectrum, and a high-frequency cutoff that arises from the asymptotic behaviour of the dielectric constant.Comment: 4 pages, RevTeX, 2 figures (.eps file) included with graphics.sty. Major revisions: physical scenario clarified, additional numerical estimate

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

Comment on gauge choices and physical variables in QED

We consider possible definitions of physical variables in QED. We demonstrate that the condition $\partial_i A_i$$=0$ is the most convenient one because it leads to path integral over physical components with local action. However, other choices, as $A_3=0$, are also possible. The standard expression for configuration space path integral in $A_3=0$ gauge is obtained starting with reduced phase space formulation. Contrary to the claims of the paper [M.Lavelle and D.McMullan,Phys. Lett. B316 (1993)172] the $A_3=0$ gauge is not overconstrained.Comment: 4 pages, SPbU-IP-94-8, Late

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

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

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of the discrete phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031 (which is to appear on J.Phys A: Math and Gen

Prime decomposition and correlation measure of finite quantum systems

Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of density matrices a complete tensor product factorization is achieved. The construction is based on the Chinese Remainder Theorem and the projective unitary representation of $Z_N$ by the discrete Heisenberg group $H_N$. The pd isomorphism is unitarily implemented and it is shown to be coassociative and to act on $H_N$ as comultiplication. Density matrices with complete pd are interpreted as grouplike elements of $H_N$. To quantify the distance of $\rho$ from its pd a trace-norm correlation index $\cal E$ is introduced and its invariance groups are determined.Comment: 9 pages LaTeX. Revised version: changes in the terminology, updates in ref

Quark-antiquark pair production in space-time dependent fields

Fermion-antifermion pair-production in the presence of classical fields is described based on the retarded and advanced fermion propagators. They are obtained by solving the equation of motion for the Dirac Green's functions with the respective boundary conditions to all orders in the field. Subsequently, various approximation schemes fit for different field configurations are explained. This includes longitudinally boost-invariant forms. Those occur frequently in the description of ultrarelativistic heavy-ion collisions in the semiclassical limit. As a next step, the gauge invariance of the expression for the expectation value of the number of produced fermion-antifermion pairs as a functional of said propagators is investigated in detail. Finally, the calculations are carried out for a longitudinally boost-invariant model-field, taking care of the last issue, especially.Comment: 32 pages, 8 figures, revised versio

Lorentz Violation and Synchrotron Radiation

We consider the radiation emitted by an ultrarelativistic charged particle moving in a magnetic field, in the presence of an additional Lorentz-violating interaction. In contrast with prior work, we treat a form of Lorentz violation that is represented by a renormalizable operator. Neglecting the radiative reaction force, the particle's trajectory can be determined exactly. The resulting orbit is generally noncircular and does not lie in the place perpendicular to the magnetic field. We do not consider any Lorentz violation in the electromagnetic sector, so the radiation from the accelerated charge can be determined by standard means, and the radiation spectrum will exhibit a Lorentz-violating directional dependence. Using data on emission from the Crab nebula, we can set a bound on a particular combination of Lorentz-violating coefficients at the $6\times10^{-20}$ level.Comment: 14 page

Hybrid noiseless subsystems for quantum communication over optical fibers

We derive the general structure of noiseless subsystems for optical radiation contained in a sequence of pulses undergoing collective depolarization in an optical fiber. This result is used to identify optimal ways to implement quantum communication over a collectively depolarizing channel, which in general combine various degrees of freedom, such as polarization and phase, into joint hybrid schemes for protecting quantum coherence.Comment: 5 pages, 1 figur