Historical research guide · 0865 · 2016
Finite difference computation of Casimir forces
Fabrizio Pinto
In one minute
Fabrizio Pinto works on computing Casimir forces — the pull two surfaces feel in vacuum because the zero-point field in the gap between them is not the same as the field outside. For sixty years the only trustworthy formula, Lifshitz’s, covered just two flat slabs facing each other, and real devices are never that. This invited paper traces the story from Casimir’s 1948 result to the moment in 2007 when a group at MIT showed that ordinary classical electromagnetism software can be retooled to compute Casimir forces in any geometry at all. Pinto’s own laboratory then takes the plainest of those methods, finite differencing, and runs it on ordinary computers, recovering the Lifshitz answer for parallel slabs and extending it to layered coatings. He lists what to point it at next: membranes bent by Casimir pressure, anisotropic materials that twist as well as pull, nanotube energy storage, and engine cycles that modulate the force in time. His closing image measures the distance travelled — these forces now hold a climbing human on smooth glass.
Connection
Chapter 2 says the vacuum is a real medium whose structure can be altered by the shapes you put in it, and this is the paper that says what it takes to calculate that alteration for a shape you actually intend to build. Chapter 6 gets the two mechanisms it needs stated plainly by a specialist: modulating the Casimir force in time is the principle a vacuum nano-engine runs on, and van der Waals gaps in telescoping nanotube arrays are a candidate energy store with a density above chemical batteries. Chapter 1 gets the measurement history in one place, from Casimir and Lifshitz to the sphere-plane experiments everybody actually performs.
From the source
Lifshitz’s 1955 stochastic-field calculation remains the standard solution for the dispersion force between two semi-infinite dielectric slabs, and using it requires knowing the complex dielectric function of the interacting materials across the whole frequency range.Sect. 1, Introduction
The field changed in 2007, when researchers at MIT and their collaborators introduced a numerical imaginary-frequency Green’s function method: it gave both a path to computing dispersion forces in any geometry and the result that the algorithm can be built, with relatively little modification, on procedures already known from classical electromagnetism.Sect. 2, Dispersion force computation: challenges and opportunities
Plain finite differencing, run on readily available computers rather than on competitive machines, converges to the available analytic solution in the one-dimensional case, handles dielectric boundaries that do not fall on mesh points, and generalises to one-dimensional multilayers; a non-standard finite-difference scheme was also identified that exactly reproduces the necessary discrete Green’s functions.Sect. 3.1 and Sect. 3.2
The ability to alter the magnitude and the sign of the Casimir force in time is the crucial principle for implementing thermodynamic nano-engines; the most realistic proposal uses the dependence of dispersion forces on illumination, verified by Arnold, Hunklinger and Dransfeld and confirmed years later by atomic force microscope methods, and what is missing is numerical models realistic enough to account for the mutual spectral perturbation of moving boundaries.Abstract; Sect. 4.7, Nanomechanical engine cycles
Robert Forward proposed in 1984 that the van der Waals interaction could serve as a reservoir for energy storage; ordinary surfaces at realistic gap widths fall far short of chemical batteries, but arrays of vertical telescoping nanotubes, with their much higher specific surface and much smaller gap, could store energy at densities even higher than chemical storage.Sect. 5.4, Energy storage and conversion
The Casimir effect occurs in classical fields as well as quantised ones, the clearest demonstration being the acoustic Casimir effect, where broadband noise from compression drivers is given a spectrum the experimenter chooses; because sound is so much slower than light the gaps are about one centimetre, and non-parallel and other geometries remain unexplored in both theory and experiment.Sect. 4.8, Acoustic Casimir effect
The way in
https://doi.org/10.1088/1742-6596/738/1/012134How to cite it
Fabrizio Pinto (2016) Finite difference computation of Casimir forces doi:10.1088/1742-6596/738/1/012134