Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

On Casimir and Helmholtz Fluctuation-Induced Forces in Micro- and Nano-Systems: Survey of Some Basic Results

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.

Attractive and Repulsive Fluctuation-Induced Pressure in Peptide Films Deposited on Semiconductor Substrates

We consider the fluctuation-induced (Casimir) pressure in peptide films deposited on GaAs, Ge, and ZnS substrates which are either in a dielectric or metallic state. The calculations of the Casimir pressure are performed in the framework of the fundamental Lifshitz theory employing the frequency-dependent dielectric permittivities of all involved materials. The electric conductivity of semiconductor substrates is taken into account within the experimentally and thermodynamically consistent approach. According to our results, the Casimir pressure in peptide films deposited on dielectric-type semiconductor substrates vanishes for some definite film thickness and is repulsive for thinner and attractive for thicker films. The dependence of this effect on the fraction of water in the film and on the static dielectric permittivity of the semiconductor substrate is determined. For the metallic-type semiconductor substrates, the Casimir pressure in peptide coatings is shown to be always repulsive. The possible applications of these results to the problem of stability of thin coatings in microdevices are discussed.

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights into the processes involved. We clarify that the form of the effective Hamiltonian depends on the field states considered, and consequently different expressions can be obtained, each of them with a well-defined range of validity and possible applications. We also apply our results to some specific cases, mainly the Lamb shift, the Casimir-Polder atom-surface interaction, and the dispersion interactions between atoms, molecules, or, in general, polarizable bodies.

Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range

We consider axionlike particles as the most probable constituents of dark matter, the Yukawa-type corrections to Newton’s gravitational law and constraints on their parameters following from astrophysics and different laboratory experiments. After a brief discussion of the results by Prof. Yu. N. Gnedin in this field, we turn our attention to the recent experiment on measuring the differential Casimir force between Au-coated surfaces of a sphere and the top and bottom of rectangular trenches. In this experiment, the Casimir force was measured over an unusually wide separation region from 0.2 to 8μm and compared with the exact theory based on first principles of quantum electrodynamics at nonzero temperature. We use the measure of agreement between experiment and theory to obtain the constraints on the coupling constant of axionlike particles to nucleons and on the interaction strength of a Yukawa-type interaction. The constraints obtained on the axion-to-nucleon coupling constant and on the strength of a Yukawa interaction are stronger by factors of 4 and 24, respectively, than those found previously from gravitational experiments and measurements of the Casimir force but weaker than the constraints following from a differential measurement where the Casimir force was nullified. Some other already performed and planned experiments aimed at searching for axions and non-Newtonian gravity are discussed, and their prospects are evaluated.