615 research outputs found

### Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$
space-time dimensions, coupled to domain-wall like defects with a smooth shape.
We show that those effects induce non trivial contributions to the
(shape-dependent) energy of the domain walls. For a single defect, we study the
divergences in the corresponding self-energy, and also consider the role of the
massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling
the Dirac field to an external gauge field. For two defects, we show that the
Dirac field induces a non trivial, Casimir-like effect between them, and
provide an exact expression for that interaction in the case of two
straight-line parallel defects. As is the case for the Casimir interaction
energy, the result is finite and unambiguous.Comment: 17 pages, 1 figur

### Vacuum fluctuations and generalized boundary conditions

We present a study of the static and dynamical Casimir effects for a quantum
field theory satisfying generalized Robin boundary condition, of a kind that
arises naturally within the context of quantum circuits. Since those conditions
may also be relevant to measurements of the dynamical Casimir effect, we
evaluate their role in the concrete example of a real scalar field in 1+1
dimensions, a system which has a well-known mechanical analogue involving a
loaded string.Comment: 8 pages, 1 figur

### Derivative expansion for the Casimir effect at zero and finite temperature in $d+1$ dimensions

We apply the derivative expansion approach to the Casimir effect for a real
scalar field in $d$ spatial dimensions, to calculate the next to leading order
term in that expansion, namely, the first correction to the proximity force
approximation. The field satisfies either Dirichlet or Neumann boundary
conditions on two static mirrors, one of them flat and the other gently curved.
We show that, for Dirichlet boundary conditions, the next to leading order term
in the Casimir energy is of quadratic order in derivatives, regardless of the
number of dimensions. Therefore it is local, and determined by a single
coefficient. We show that the same holds true, if $d \neq 2$, for a field which
satisfies Neumann conditions. When $d=2$, the next to leading order term
becomes nonlocal in coordinate space, a manifestation of the existence of a
gapless excitation (which do exist also for $d> 2$, but produce sub-leading
terms).
We also consider a derivative expansion approach including thermal
fluctuations of the scalar field. We show that, for Dirichlet mirrors, the next
to leading order term in the free energy is also local for any temperature $T$.
Besides, it interpolates between the proper limits: when $T \to 0$ it tends to
the one we had calculated for the Casimir energy in $d$ dimensions, while for
$T \to \infty$ it corresponds to the one for a theory in $d-1$ dimensions,
because of the expected dimensional reduction at high temperatures. For Neumann
mirrors in $d=3$, we find a nonlocal next to leading order term for any $T>0$.Comment: 18 pages, 6 figures. Version to appear in Phys. Rev.

### The effect of concurrent geometry and roughness in interacting surfaces

We study the interaction energy between two surfaces, one of them flat, the
other describable as the composition of a small-amplitude corrugation and a
slightly curved, smooth surface. The corrugation, represented by a spatially
random variable, involves Fourier wavelengths shorter than the (local)
curvature radii of the smooth component of the surface. After averaging the
interaction energy over the corrugation distribution, we obtain an expression
which only depends on the smooth component. We then approximate that functional
by means of a derivative expansion, calculating explicitly the leading and
next-to-leading order terms in that approximation scheme. We analyze the
resulting interplay between shape and roughness corrections for some specific
corrugation models in the cases of electrostatic and Casimir interactions.Comment: 14 pages, 3 figure

### The derivative expansion approach to the interaction between close surfaces

The derivative expansion approach to the calculation of the interaction
between two surfaces, is a generalization of the proximity force approximation,
a technique of widespread use in different areas of physics. The derivative
expansion has so far been applied to seemingly unrelated problems in different
areas; it is our principal aim here to present the approach in its full
generality. To that end, we introduce an unified setting, which is independent
of any particular application, provide a formal derivation of the derivative
expansion in that general setting, and study some its properties. With a view
on the possible application of the derivative expansion to other areas, like
nuclear and colloidal physics, we also discuss the relation between the
derivative expansion and some time-honoured uncontrolled approximations used in
those contexts. By putting them under similar terms as the derivative
expansion, we believe that the path is open to the calculation of next to
leading order corrections also for those contexts. We also review some results
obtained within the derivative expansion, by applying it to different concrete
examples and highlighting some important points.Comment: Minor changes, version to appear in Phys. Rev.

### Inertial forces and dissipation on accelerated boundaries

We study dissipative effects due to inertial forces acting on matter fields
confined to accelerated boundaries in $1+1$, $2+1$, and $3+1$ dimensions. These
matter fields describe the internal degrees of freedom of `mirrors' and impose,
on the surfaces where they are defined, boundary conditions on a fluctuating
`vacuum' field. We construct different models, involving either scalar or Dirac
matter fields coupled to a vacuum scalar field, and use effective action
techniques to calculate the strength of dissipation. In the case of massless
Dirac fields, the results could be used to describe the inertial forces on an
accelerated graphene sheet.Comment: 7 pages, no figure

### Electrostatic Interaction due to Patch Potentials on Smooth Conducting Surfaces

We evaluate the electrostatic interaction energy between two surfaces, one
flat and the other slightly curved, in terms of the two-point autocorrelation
functions for patch potentials on each one of them, and of a single function
$\psi$ which defines the curved surface. The resulting interaction energy, a
functional of $\psi$, is evaluated up to the second order in a derivative
expansion approach. We derive explicit formulae for the coefficients of that
expansion as simple integrals involving the autocorrelation functions, and
evaluate them for some relevant patch-potential profiles and geometriesComment: Minor changes, version to be published in Phys. Rev.

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