2,218 research outputs found
Functional treatment of quantum scattering via the dynamical principle
A careful functional treatment of quantum scattering is given using
Schwinger's dynamical principle which involves a functional differentiation
operation applied to a generating functional written in closed form. For long
range interactions, such as for the Coulomb one, it is shown that this
expression may be used to obtain explicitly the asymptotic "free" modified
Green function near the energy shell.Comment: 7 page
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
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
Unitary equivalence between ordinary intelligent states and generalized intelligent states
Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty
relation involving two noncommuting observables {A, B}, whereas generalized
intelligent states (GIS) do so in the more generalized uncertainty relation,
the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs.
However, if there exists a unitary evolution U that transforms the operators
{A, B} to a new pair of operators in a rotation form, it is shown that an
arbitrary GIS can be generated by applying the rotation operator U to a certain
OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs.
It is the case, for example, with the su(2) and the su(1,1) algebra that have
been extensively studied particularly in quantum optics. When these algebras
are represented by two bosonic operators (nondegenerate case), or by a single
bosonic operator (degenerate case), the rotation, or pseudo-rotation, operator
U corresponds to phase shift, beam splitting, or parametric amplification,
depending on two observables {A, B}.Comment: published version, 4 page
Unitary equivalence between ordinary intelligent states and generalized intelligent states
Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty
relation involving two noncommuting observables {A, B}, whereas generalized
intelligent states (GIS) do so in the more generalized uncertainty relation,
the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs.
However, if there exists a unitary evolution U that transforms the operators
{A, B} to a new pair of operators in a rotation form, it is shown that an
arbitrary GIS can be generated by applying the rotation operator U to a certain
OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs.
It is the case, for example, with the su(2) and the su(1,1) algebra that have
been extensively studied particularly in quantum optics. When these algebras
are represented by two bosonic operators (nondegenerate case), or by a single
bosonic operator (degenerate case), the rotation, or pseudo-rotation, operator
U corresponds to phase shift, beam splitting, or parametric amplification,
depending on two observables {A, B}.Comment: published version, 4 page
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
Vacuum polarization induced by a uniformly accelerated charge
We consider a point charge fixed in the Rindler coordinates which describe a
uniformly accelerated frame. We determine an integral expression of the induced
charge density due to the vacuum polarization at the first order in the fine
structure constant. In the case where the acceleration is weak, we give
explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys
Exact factorization of the time-dependent electron-nuclear wavefunction
We present an exact decomposition of the complete wavefunction for a system
of nuclei and electrons evolving in a time-dependent external potential. We
derive formally exact equations for the nuclear and electronic wavefunctions
that lead to rigorous definitions of a time-dependent potential energy surface
(TDPES) and a time-dependent geometric phase. For the molecular ion
exposed to a laser field, the TDPES proves to be a useful interpretive tool to
identify different mechanisms of dissociation.Comment: 4 pages, 2 figure
Casimir Force between a Small Dielectric Sphere and a Dielectric Wall
The possibility of repulsive Casimir forces between small metal spheres and a
dielectric half-space is discussed. We treat a model in which the spheres have
a dielectric function given by the Drude model, and the radius of the sphere is
small compared to the corresponding plasma wavelength. The half-space is also
described by the same model, but with a different plasma frequency. We find
that in the retarded limit, the force is quasi-oscillatory. This leads to the
prediction of stable equilibrium points at which the sphere could levitate in
the Earth's gravitational field. This seems to lead to the possibility of an
experimental test of the model. The effects of finite temperature on the force
are also studied, and found to be rather small at room temperature. However,
thermally activated transitions between equilibrium points could be significant
at room temperature.Comment: 16 pages, 5 figure
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