6,546 research outputs found
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
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 dimensions
We apply the derivative expansion approach to the Casimir effect for a real
scalar field in 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 , for a field which
satisfies Neumann conditions. When , 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 , 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 .
Besides, it interpolates between the proper limits: when it tends to
the one we had calculated for the Casimir energy in dimensions, while for
it corresponds to the one for a theory in dimensions,
because of the expected dimensional reduction at high temperatures. For Neumann
mirrors in , we find a nonlocal next to leading order term for any .Comment: 18 pages, 6 figures. Version to appear in Phys. Rev.
Radiatively Induced Breaking of Conformal Symmetry in a Superpotential
Radiatively induced symmetry breaking is considered for a toy model with one
scalar and one fermion field unified in a superfield. It is shown that the
classical quartic self-interaction of the superfield possesses a quantum
infrared singularity. Application of the Coleman-Weinberg mechanism for
effective potential leads to the appearance of condensates and masses for both
scalar and fermion components. That induces a spontaneous breaking of the
initial classical symmetries: the supersymmetry and the conformal one. The
energy scales for the scalar and fermion condensates appear to be of the same
order, while the renormalization scale is many orders of magnitude higher. A
possibility to relate the considered toy model to conformal symmetry breaking
in the Standard Model is discussed.Comment: Improved final version with new references and misprints corrected, 9
pages , no 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 , , and 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
Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors
We evaluate the difference between the Casimir free energies corresponding to
either grounded or isolated perfect conductors, at high temperatures. We show
that a general and simple expression for that difference can be given, in terms
of the electrostatic capacitance matrix for the system of conductors. For the
case of close conductors, we provide approximate expressions for that
difference, by evaluating the capacitance matrix using the proximity force
approximation. Since the high-temperature limit for the Casimir free energy for
a medium described by a frequency-dependent conductivity diverging at zero
frequency coincides with that of an isolated conductor, our results may shed
light on the corrections to the Casimir force in the presence of real
materials.Comment: 7 page
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