257 research outputs found
An exact solution for the Hawking effect in a dispersive fluid
We consider the wave equation for sound in a moving fluid with a fourth-order
anomalous dispersion relation. The velocity of the fluid is a linear function
of position, giving two points in the flow where the fluid velocity matches the
group velocity of low-frequency waves. We find the exact solution for wave
propagation in the flow. The scattering shows amplification of classical waves,
leading to spontaneous emission when the waves are quantized. In the
dispersionless limit the system corresponds to a 1+1-dimensional black-hole or
white-hole binary and there is a thermal spectrum of Hawking radiation from
each horizon. Dispersion changes the scattering coefficients so that the
quantum emission is no longer thermal. The scattering coefficients were
previously obtained by Busch and Parentani in a study of dispersive fields in
de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further
details of the wave propagation in this exactly solvable case, where our focus
is on laboratory systems.Comment: 18 pages, minor change
Electromagnetic energy-momentum in dispersive media
The standard derivations of electromagnetic energy and momentum in media take
Maxwell's equations as the starting point. It is well known that for dispersive
media this approach does not directly yield exact expressions for the energy
and momentum densities. Although Maxwell's equations fully describe
electromagnetic fields, the general approach to conserved quantities in field
theory is not based on the field equations, but rather on the action. Here an
action principle for macroscopic electromagnetism in dispersive, lossless media
is used to derive the exact conserved energy-momentum tensor. The time-averaged
energy density reduces to Brillouin's simple formula when the fields are
monochromatic. The momentum density is not given by the familiar Minkowski
expression , even for time-averaged monochromatic
fields. The results are unaffected by the debate over momentum balance in
light-matter interactions.Comment: 7 pages. Incorporates the Erratum to the published versio
All-frequency reflectionlessness
We derive planar permittivity profiles that do not reflect perpendicularly
exiting radiation of any frequency. The materials obey the Kramers-Kronig
relations and have no regions of gain. Reduction of the Casimir force by means
of such materials is also discussed.Comment: 7 page
No quantum friction between uniformly moving plates
The Casimir forces between two plates moving parallel to each other are found
by calculating the vacuum electromagnetic stress tensor. The perpendicular
force between the plates is modified by the motion but there is no lateral
force on the plates. Electromagnetic vacuum fluctuations do not therefore give
rise to "quantum friction" in this case, contrary to previous assertions. The
result shows that the Casimir-Polder force on a particle moving at constant
speed parallel to a plate also has no lateral component.Comment: 17 pages. Final, published versio
Thermal energies of classical and quantum damped oscillators coupled to reservoirs
We consider the global thermal state of classical and quantum harmonic
oscillators that interact with a reservoir. Ohmic damping of the oscillator can
be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic
damping is conveniently treated with a continuum reservoir of harmonic
oscillators. Using the diagonalized Hamiltonian of the total system, we
calculate a number of thermodynamic quantities for the damped oscillator: the
mean force internal energy, mean force free energy, and another internal energy
based on the free-oscillator Hamiltonian. The classical mean force energy is
equal to that of a free oscillator, for both Ohmic and non-Ohmic damping and no
matter how strong the coupling to the reservoir. In contrast, the quantum mean
force energy depends on the details of the damping and diverges for strictly
Ohmic damping. These results give additional insight into the steady-state
thermodynamics of open systems with arbitrarily strong coupling to a reservoir,
complementing results for energies derived within dynamical approaches (e.g.
master equations) in the weak-coupling regime.Comment: 13 page
Optical angular momentum in dispersive media
The angular momentum density and flux of light in a dispersive, rotationally
symmetric medium are derived from Noether's theorem. Optical angular momentum
in a dispersive medium has no simple relation to optical linear momentum, even
if the medium is homogeneous. A circularly polarized monochromatic beam in a
homogeneous, dispersive medium carries a spin angular momentum of
per energy , as in vacuum. This result demonstrates the
non-trivial interplay of dispersive contributions to optical angular momentum
and energy.Comment: 4 page
- β¦