1,680 research outputs found
Manipulating lightcone fluctuations in an analogue cosmic string
We study the flight time fluctuations in an anisotropic medium inspired by a
cosmic string with an effective fluctuating refractive index caused by
fluctuating vacuum electric fields, which are analogous to the lightcone
fluctuations due to fluctuating spacetime metric when gravity is quantized. The
medium can be realized as a metamaterial that mimics a cosmic string in the
sense of transformation optics. For a probe light close to the analogue string,
the flight time variance is times that in a normal homogeneous and
isotropic medium, where is a parameter characterizing the deficit angle
of the spacetime of a cosmic string. The parameter , which is always
greater than unity for a real cosmic string, is determined by the dielectric
properties of the metamaterial for an analogue string. Therefore, the flight
time fluctuations of a probe light can be manipulated by changing the electric
permittivity and magnetic permeability of the analogue medium. We argue that it
seems possible to fabricate a metamaterial that mimics a cosmic string with a
large in laboratory so that a currently observable flight time variance
might be achieved.Comment: 13 pages, 1 figur
Geometrically Partial actions
We introduce "geometric" partial comodules over coalgebras in monoidal
categories, as an alternative notion to the notion of partial action and
coaction of a Hopf algebra introduced by Caenepeel and Janssen. The name is
motivated by the fact that our new notion suits better if one wants to describe
phenomena of partial actions in algebraic geometry. Under mild conditions, the
category of geometric partial comodules is shown to be complete and cocomplete
and the category of partial comodules over a Hopf algebra is lax monoidal. We
develop a Hopf-Galois theory for geometric partial coactions to illustrate that
our new notion might be a useful additional tool in Hopf algebra theory.Comment: revised version; improved presentation; stronger version of
"fundamental theorem" for partial comodules. Version accepted for publication
in "Transactions of the American Mathematical Society". Updated reference
Quantum gravitational interaction between a polarizable object and a boundary
We investigate the interaction caused by quantum gravitational vacuum
fluctuations between a gravitationally polarizable object and a gravitational
boundary, and find a position-dependent energy shift of the object, which
induces a force in close analogy to the Casimir-Polder force in the
electromagnetic case. For a Dirichlet boundary, the explicit form of the
quantum gravitational potential for the polarizable object in its ground-state
is worked out and is found to behave like in the near regime, and
in the far regime, where is the distance to the boundary. Taking a
Bose-Einstein condensate as a gravitationally polarizable object, we find that
the relative correction to the radius caused by fluctuating quantum
gravitational waves in vacuum is of order . Although far too small to
observe in comparison with its electromagnetic counterpart, it is nevertheless
of the order of the gravitational strain caused by a recently detected black
hole merger on the arms of the LIGO.Comment: 11 pages, no figure
Quantum correction to classical gravitational interaction between two polarizable objects
When gravity is quantized, there inevitably exist quantum gravitational
vacuum fluctuations which induce quadrupole moments in gravitationally
polarizable objects and produce a quantum correction to the classical Newtonian
interaction between them. Here, based upon linearized quantum gravity and the
leading-order perturbation theory, we study, from a quantum field-theoretic
prospect, this quantum correction between a pair of gravitationally polarizable
objects treated as two-level harmonic oscillators. We find that the interaction
potential behaves like in the retarded regime and in the
near regime. Our result agrees with what was recently obtained in different
approaches. Our study seems to indicate that linearized quantum gravity is
robust in dealing with quantum gravitational effects at low energies.Comment: 10 pages. Accepted for publication in PL
Interaction between two gravitationally polarizable objects induced by thermal bath of gravitons
The quadrupole-quadrupole interaction between a pair of gravitationally
polarizable objects induced by vacuum fluctuations of the quantum linearized
gravitational field is first obtained with a relatively simple method, which is
then used to investigate the contribution of thermal fluctuations of a bath of
gravitons to the interaction at temperature . Our result shows that, in the
high temperature limit, the contribution of thermal fluctuations dominates over
that of vacuum fluctuations and the interaction potential behaves like , where is the separation between the objects, and in the low
temperature limit, the contribution of thermal fluctuations is proportional to
, which only provides a small correction to the interaction induced
by zero-point fluctuations.Comment: 11 pages. Accepted by PR
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