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Title: CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries

Abstract

The so-called Casimir effect is one of the most interesting macro-quantum effects. Being negligible on the macro-scale it becomes a governing factor below structure sizes of 1 {mu}m where it accounts for typically 100 kN m-2. The force does not depend on gravity, or electric charge but solely on the materials properties, and geometrical shape. This makes the effect a strong candidate for micro(nano)-mechanical devices M(N)EMS. Despite a long history of research the theory lacks a uniform description valid for arbitrary geometries which retards technical application. We present an advanced state-of-the-art numerical tool overcoming all the usual geometrical restrictions, capable of calculating arbitrary 3D geometries by utilizing the Casimir Polder approximation for the Casimir force.

Authors:
;  [1]
  1. ARC Seibersdorf research Gmbh, Business field Space Propulsion, A-2444 Seibersdorf (Austria)
Publication Date:
OSTI Identifier:
21054531
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 880; Journal Issue: 1; Conference: International forum-STAIF 2007: 11. conference on thermophysics applications in microgravity; 24. symposium on space nuclear power and propulsion; 5. conference on human/robotic technology and the vision for space exploration; 5. symposium on space colonization; 4. symposium on new frontiers and future concepts, Albuquerque, NM (United States), 11-15 Feb 2007; Other Information: DOI: 10.1063/1.2437561; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CALCULATION METHODS; CASIMIR EFFECT; GEOMETRY; NUMERICAL ANALYSIS; QUANTUM ELECTRODYNAMICS; SHAPE; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Sedmik, Rene, and Tajmar, Martin. CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries. United States: N. p., 2007. Web. doi:10.1063/1.2437561.
Sedmik, Rene, & Tajmar, Martin. CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries. United States. doi:10.1063/1.2437561.
Sedmik, Rene, and Tajmar, Martin. Tue . "CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries". United States. doi:10.1063/1.2437561.
@article{osti_21054531,
title = {CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries},
author = {Sedmik, Rene and Tajmar, Martin},
abstractNote = {The so-called Casimir effect is one of the most interesting macro-quantum effects. Being negligible on the macro-scale it becomes a governing factor below structure sizes of 1 {mu}m where it accounts for typically 100 kN m-2. The force does not depend on gravity, or electric charge but solely on the materials properties, and geometrical shape. This makes the effect a strong candidate for micro(nano)-mechanical devices M(N)EMS. Despite a long history of research the theory lacks a uniform description valid for arbitrary geometries which retards technical application. We present an advanced state-of-the-art numerical tool overcoming all the usual geometrical restrictions, capable of calculating arbitrary 3D geometries by utilizing the Casimir Polder approximation for the Casimir force.},
doi = {10.1063/1.2437561},
journal = {AIP Conference Proceedings},
number = 1,
volume = 880,
place = {United States},
year = {Tue Jan 30 00:00:00 EST 2007},
month = {Tue Jan 30 00:00:00 EST 2007}
}
  • We prove that the nonretarded Casimir-Polder potential of a particle in an energy eigenstate (hence in thermal nonequilibrium) is independent of the environment temperature for a well-conducting body of arbitrary shape. This is true even when the thermal photon numbers at the relevant atomic transition energies are large. A compact expression is obtained for the temperature-independent potential, which can greatly simplify calculations in nontrivial geometries for experimentally relevant systems such as Rydberg atoms and polar molecules. We give criteria for the validity of our temperature-independent result and derive general expressions for its leading corrections. They are illustrated by numerical studiesmore » of a particle near a gold sphere or inside a gold cylindrical cavity.« less
  • We critically discuss whether and under what conditions Lifshitz theory may be used to describe thermal Casimir-Polder forces on atoms or molecules. An exact treatment of the atom-field coupling reveals that for a ground-state atom (molecule), terms associated with virtual-photon absorption lead to a deviation from the traditional Lifshitz result; they are identified as a signature of nonequilibrium dynamics. Even the equilibrium force on a thermalized atom (molecule) may be overestimated when using the ground-state polarizability instead of its thermal counterpart.
  • We consider the Casimir–Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate the overall two- and three-body contributions to the macroscopic Casimir–Polder and Casimir force, and to compare them with each other, for the two following geometries: metal nanoparticle/half-space and half-space/half-space, where all themore » materials are assumed perfect conductors. The above evaluation is obtained by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles). In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known non applicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.« less
  • Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superpositionmore » of force components that are related to the electronic density matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.« less
  • We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.