Fluctuations of Fluctuation-Induced "Casimir" Forces

We consider the quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated to the force experienced by the atom considered as a polarizable body in an electromagnetic field, and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. ...

We study the spatial fluctuations of the Casimir-Polder force experienced by an atom or a small sphere moved above a metallic plate at fixed separation distance. We demonstrate that unlike the mean force, the magnitude of these fluctuations crucially relies on the relaxation of conduction electron in the metallic bulk, and even achieves values that differ by orders of magnitude depending on the amount of dissipation. We also discover that fluctuations suffer a spectacular dec...

The Casimir force, which results from the confinement of the quantum mechanical zero-point fluctuations of the electromagnetic fields, has received significant attention in recent years for its effect on micro- and nano-scale mechanical systems. With few exceptions, experimental observations have been limited to conductive bodies interacting separated by vacuum or air. However, interesting phenomena including repulsive forces are expected to exist in certain circumstances bet...

On the examples of the quantum-electrodynamical Casimir force, as well as critical Casimir and Helmholtz forces, we present a review of some results available for the class of fluctuation induced forces. In addition, we also concisely present examples of other such fluctuation-induced forces. On the instance of the Ising model we discuss the connection between the Casimir and Helmholtz forces. We discuss the importance of the presented results for the nanotechnology, and espe...

Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrary shaped objects immersed in a scalar or vector fluctuating field in arbitrary dimensions. Finite-temperature corrections are derived and the results are compared in first order with weak coupling regime in scattering method. The generalization to a massive vector field is also investigated.

Casimir forces can appear between intrusions placed in different media driven by several fluctuation mechanisms, either in equilibrium or out of it. Herein, we develop a general formalism to obtain such forces from the dynamical equations of the fluctuating medium, the statistical properties of the driving noise, and the boundary conditions of the intrusions (which simulate the interaction between the intrusions and the medium). As a result, an explicit formula for the Casimi...

The famous Johnson-Nyquist formula relating noise current to conductance has a microscopic generalization relating noise current density to microscopic conductivity, with corollary relations governing noise in the components of the electromagnetic fields. These relations, known collectively in physics as fluctuation-dissipation relations, form the basis of the modern understanding of fluctuation-induced phenomena, a field of burgeoning importance in experimental physics and n...

The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observ...

Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. The force falls off with slab separation $d$ as $k_B T/d$ (at temperature $T$, and in all spatial dimensions), but can be attractive or repulsive. Unlike the equili...

It is predicted that in force microscopy the quantum fluctuations responsible for the Casimir force can be directly observed as temperature-independent force fluctuations having spectral density $9\pi/(40\ln(4/e)) \hbar \delta k$, where $\hbar$ is Planck's constant and $\delta k$ is the observed change in spring constant as the microscope tip approaches a sample. For typical operating parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz of bandwidth...