17 research outputs found
Anomalies and symmetries of the regularized action
We show that the Pauli-Villars regularized action for a scalar field in a
gravitational background in 1+1 dimensions has, for any value of the cutoff M,
a symmetry which involves non-local transformations of the regulator field plus
(local) Weyl transformations of the metric tensor. These transformations, an
extension to the regularized action of the usual Weyl symmetry transformations
of the classical action, lead to a new interpretation of the conformal anomaly
in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the
Jacobian is automatically regularized, and yields the correct result when the
masses of the regulators tend to infinity. In this limit the transformations,
which are non-local in a scale of 1/M, become the usual Weyl transformation of
the metric. We also present the example of the chiral anomaly in 1+1
dimensions.Comment: 13 pages, Late
On the spatial dependence of Casimir friction in graphene
We study the spatial properties of the Casimir friction phenomenon for an
atom moving at a non-relativistic constant velocity parallel to a planar
graphene sheet. The coupling of the atom to the vacuum electromagnetic (EM)
field is implemented by an electric dipole term, plus a R\"ontgen term. We
study the fermion pair production, evaluating the angular dependence of the
fermion emission probability. The phenomenon exhibits a threshold: it only
exists when the speed of the sliding motion is larger than the Fermi velocity
of the medium.Comment: 10 pages, LaTe
Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion
We review the derivative expansion (DE) method in Casimir physics, an
approach which extends the proximity force approximation (PFA). After
introducing and motivating the DE in contexts other than the Casimir effect, we
present different examples which correspond to that realm. We focus on
different particular geometries, boundary conditions, types of fields, and
quantum and thermal fluctuations. Besides providing various examples where the
method can be applied, we discuss a concrete example for which the DE cannot be
applied; namely, the case of perfect Neumann conditions in 2 + 1 dimensions. By
the same example, we show how a more realistic type of boundary condition
circumvents the problem. We also comment on the application of the DE to the
Casimir-Polder interaction which provides a broader perspective on
particle-surface interactions.Comment: 20 pages, 1 figure. This is a review based on our works on the
subjec
Motion induced excitation and electromagnetic radiation from an atom facing a thin mirror
We evaluate the probability of (de-)excitation and photon emission from a
neutral, moving, non-relativistic atom, coupled to the quantum electromagnetic
field and in the presence of a thin, perfectly conducting plane ("mirror").
These results extend, to a more realistic model, the ones we had presented for
a scalar model, where the would-be electron was described by a scalar variable,
coupled to an (also scalar) vacuum field. The latter was subjected to either
Dirichlet or Neumann conditions on a plane. In our evaluation of the
spontaneous emission rate produced when the accelerated atom is initially in an
excited state, we pay attention to its comparison with the somewhat opposite
situation, namely, an atom at rest facing a moving mirror.Comment: 10 pages, 5 figures. Version accepted to be published in Phys. Rev.
Functional approach to quantum friction: effective action and dissipative force
We study the Casimir friction due to the relative, uniform, lateral motion of
two parallel semitransparent mirrors coupled to a vacuum real scalar field,
. We follow a functional approach, whereby nonlocal terms in the action
for , concentrated on the mirrors' locii, appear after functional
integration of the microscopic degrees of freedom. This action for ,
which incorporates the relevant properties of the mirrors, is then used as the
starting point for two complementary evaluations: Firstly, we calculate the {
in-out} effective action for the system, which develops an imaginary part,
hence a non-vanishing probability for the decay (because of friction) of the
initial vacuum state. Secondly, we evaluate another observable: the vacuum
expectation value of the frictional force, using the { in-in} or Closed Time
Path formalism. Explicit results are presented for zero-width mirrors and
half-spaces, in a model where the microscopic degrees of freedom at the mirrors
are a set of identical quantum harmonic oscillators, linearly coupled to $\phi
Fourth order perturbative expansion for the Casimir energy with a slightly deformed plate
We apply a perturbative approach to evaluate the Casimir energy for a
massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary
conditions on two surfaces. One of the surfaces is assumed to be flat, while
the other corresponds to a small deformation, described by a single function
, of a flat mirror. The perturbative expansion is carried out up to the
fourth order in the deformation , and the results are applied to the
calculation of the Casimir energy for corrugated mirrors in front of a plane.
We also reconsider the proximity force approximation within the context of this
expansion.Comment: 10 pages, 3 figures. Version to appear in Phys. Rev.
Derivative expansion of the electromagnetic Casimir energy for two thin mirrors
We extend our previous work on a derivative expansion for the Casimir energy,
to the case of the electromagnetic field coupled to two thin, imperfect
mirrors. The latter are described by means of vacuum polarization tensors
localized on the mirrors. We apply the results so obtained to compute the first
correction to the proximity force approximation to the static Casimir effect.Comment: Version to appear in Phys. Rev.
The proximity force approximation for the Casimir energy as a derivative expansion
The proximity force approximation (PFA) has been widely used as a tool to
evaluate the Casimir force between smooth objects at small distances. In spite
of being intuitively easy to grasp, it is generally believed to be an
uncontrolled approximation. Indeed, its validity has only been tested in
particular examples, by confronting its predictions with the next to leading
order (NTLO) correction extracted from numerical or analytical solutions
obtained without using the PFA. In this article we show that the PFA and its
NTLO correction may be derived within a single framework, as the first two
terms in a derivative expansion. To that effect, we consider the Casimir energy
for a vacuum scalar field with Dirichlet conditions on a smooth curved surface
described by a function in front of a plane. By regarding the Casimir
energy as a functional of , we show that the PFA is the leading term in a
derivative expansion of this functional. We also obtain the general form of
corresponding NTLO correction, which involves two derivatives of . We
show, by evaluating this correction term for particular geometries, that it
properly reproduces the known corrections to PFA obtained from exact
evaluations of the energy.Comment: Minor changes. Version to appear in Phys. Rev.
Oscillating dipole layer facing a conducting plane: a classical analogue of the dynamical Casimir effect
We study the properties of the classical electromagnetic radiation produced by two physically different yet closely related systems, which may be regarded as classical analogues of the dynamical Casimir effect. They correspond to two flat, infinite, parallel planes, one of them static and imposing perfect-conductor boundary conditions, while the other performs a rigid oscillatory motion. The systems differ just in the electrical properties of the oscillating plane: one of them is just a planar dipole layer (representing, for instance, a small-width electret). The other, instead, has a dipole layer on the side which faces the static plane, but behaves as a conductor on the other side: this can be used as a representation of a conductor endowed with patch potentials (on the side which faces the conducting plane). We evaluate, in both cases, the dissipative flux of energy between the system and its environment, showing that, at least for small mechanical oscillation amplitudes, it can be written in terms of the dipole layer autocorrelation function. We show that there are resonances as a function of the frequency of the mechanical oscillation