arXiv subjects

F. D. Mazzitelli

Publications and source records attributed to F. D. Mazzitelli.

At least 37 records · Page 2Linked to original sources

arXiv2015

Dynamical Casimir effect in superconducting circuits: a numerical approach

We present a numerical analysis of the particle creation for a quantum field in the presence of time dependent boundary conditions. Having in mind recent experiments involving superconducting circuits, we consider their description in terms of a scalar field in a one dimensional cavity satisfying generalized boundary conditions that involve a time-dependent linear combination of the field and its spatial and time derivatives. We evaluate numerically the Bogoliubov transformation between {\it in} and {\it out}-states and find that the rate of particle production strongly depends on whether the spectrum of the unperturbed cavity is equidistant or not, and also on the amplitude of the temporal oscillations of the boundary conditions. We provide analytic justifications for the different regimes found numerically.

quant-ph↗

arXiv2015

On the Derivative Expansion for the Electromagnetic Casimir Free Energy at High Temperatures

We study the contribution of the thermal zero modes to the Casimir free energy, in the case of a fluctuating electromagnetic (EM) field in the presence of real materials described by frequency-dependent, local and isotropic permittivity ($ε$) and permeability ($μ$) functions. Those zero modes, present at any finite temperature, become dominant at high temperatures, since the theory is dimensionally reduced. Our work, within the context of the Derivative Expansion (DE) approach, focusses on the emergence of non analyticities in that dimensionally reduced theory. We conclude that the DE is well defined whenever the function $Ω(ω)$, defined by $[Ω(ω)]^2 \equiv ω^2ε(ω)$, vanishes in the zero-frequency limit, for at least one of the two material media involved.

hep-th↗

arXiv2015

Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors

We calculate the Casimir interaction energy in $d=2$ spatial dimensions between two (zero-width) mirrors, one flat, and the other slightly curved, upon which {\em imperfect\/} conductor boundary conditions are imposed for an Electromagnetic (EM) field. Our main result is a second-order Derivative Expansion (DE) approximation for the Casimir energy, which is studied in different interesting limits. In particular, we focus on the emergence of a non-analyticity beyond the leading-order term in the DE, when approaching the limit of perfectly-conducting mirrors. We also show that the system considered is equivalent to a dual one, consisting of a massless real scalar field satisfying imperfect Neumann conditions (on the very same boundaries). Therefore, the results obtained for the EM field hold also true for the scalar field model

hep-th↗

arXiv2015

Area terms in entanglement entropy

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.

hep-th↗

arXiv2014

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.

hep-th↗

arXiv2014

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.

quant-ph↗

arXiv2013

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 $ψ$ which defines the curved surface. The resulting interaction energy, a functional of $ψ$, 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 geometries

hep-th↗

arXiv2013

Quantum dissipative effects in graphene-like mirrors

We study quantum dissipative effects due to the accelerated motion of a single, imperfect, zero-width mirror. It is assumed that the microscopic degrees of freedom on the mirror are confined to it, like in plasma or graphene sheets. Therefore, the mirror is described by a vacuum polarization tensor $Π_{αβ}$ concentrated on a time-dependent surface. Under certain assumptions about the microscopic model for the mirror, we obtain a rather general expression for the Euclidean effective action, a functional of the time-dependent mirror's position, in terms of two invariants that characterize the tensor $Π_{αβ}$. The final result can be written in terms of the TE and TM reflection coefficients of the mirror, with qualitatively different contributions coming from them. We apply that general expression to derive the imaginary part of the `in-out' effective action, which measures dissipative effects induced by the mirror's motion, in different models, in particular for an accelerated graphene sheet.

hep-th↗

arXiv2013

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.

hep-th↗

arXiv2012

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 $η$, of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation $η$, 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.

hep-th↗

arXiv2012

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 $T>0$.

hep-th↗

arXiv2012

An improved proximity force approximation for electrostatics

A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes. Indeed, in the so called "proximity force approximation" the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contribution of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied to different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful to discuss the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes.

physics.class-ph↗

arXiv2011

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 $ψ$ in front of a plane. By regarding the Casimir energy as a functional of $ψ$, 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 $ψ$. 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.

hep-th↗

arXiv2011

Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem

We provide a Quantum Field Theory derivation of Lifshitz formula for the Casimir force due to a fluctuating real scalar field in $d+1$ dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand-Yaglom's formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies.

hep-th↗

arXiv2011

Results from electrostatic calibrations for measuring the Casimir force in the cylinder-plane geometry

We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurement performed in the parallel plane configuration, showing that the dependence on distance of the minimizing potential, if present at all, is milder than in the sphere-plane or cylinder-plane geometries. General considerations on the interplay between the distance-dependent minimizing potential and the precision of Casimir force measurements in the range relevant to detect the thermal corrections for all geometries are finally reported.

quant-ph↗

arXiv2010

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.

hep-th↗

arXiv2010

Casimir energy between media-separated cylinders: the scalar case

We derive exact expressions for the Casimir scalar interaction energy between media-separated eccentric dielectric cylinders and for the media-separated cylinder-plane geometry using a mode-summation approach. Similarly to the electromagnetic Casimir-Lifshitz interaction energy between fluid-separated planar plates, the force between cylinders is attractive or repulsive depending on the relative values of the permittivities of the three intervening media.

quant-ph↗

arXiv2010

Low energy Quantum Gravity from the Effective Average Action

Within the effective average action approach to quantum gravity, we recover the low energy effective action as derived in the effective field theory framework, by studying the flow of possibly non-local form factors that appear in the curvature expansion of the effective average action. We restrict to the one-loop flow where progress can be made with the aid of the non-local heat kernel expansion. We discuss the possible physical implications of the scale dependent low energy effective action through the analysis of the quantum corrections to the Newtonian potential.

hep-th↗