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 d+1d+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.

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 $1+1$, $2+1$, 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

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