Control of the lateral Casimir force between corrugated surfaces

Blagov, E. V.; Mohideen, U.; Mostepanenko, V. M.

doi:10.1103/physreva.69.044103

Cited by 39 publications

(15 citation statements)

References 35 publications

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“…(14) - (16), expand the function f (x, y) in powers of x = τ t, and than integrate the obtained expansion with respect to y from x to infinity in order to find F (x) in Eq. (18) and…”

Section: New Analytical Results For the Thermal Casimir Force Betweenmentioning

confidence: 99%

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Recent Results on Thermal Casimir Force Between Dielectrics and Related Problems

Geyer

Klimchitskaya

Mostepanenko

2006

Int. J. Mod. Phys. A

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We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivity of dielectric plates is proved to lead to a violation of the Nernst heat theorem and, thus, is not related to the phenomenon of dispersion forces. The low-temperature asymptotics of the Casimir free energy, pressure and entropy are derived also in the configuration of one metal and one dielectric plate. The results are shown to be consistent with thermodynamics if the dielectric plate possesses a finite static dielectric permittivity. If the dc conductivity of a dielectric plate is taken into account this results in the violation of the Nernst heat theorem. We discuss both the experimental and theoretical results related to the Casimir interaction between metal and semiconductor with different charge carrier density. Discussions in the literature on the possible influence of spatial dispersion on the thermal Casimir force are analyzed. In conclusion, the conventional Lifshitz theory taking into account only the frequency dispersion remains the reliable foundation for the interpretation of all present experiments.

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“…(14) - (16), expand the function f (x, y) in powers of x = τ t, and than integrate the obtained expansion with respect to y from x to infinity in order to find F (x) in Eq. (18) and…”

Section: New Analytical Results For the Thermal Casimir Force Betweenmentioning

confidence: 99%

“…(22) term by term according to Eq. (18), expand the partial results in powers of x and sum up the obtained series. Thereby we obtain the following expressions:…”

Section: New Analytical Results For the Thermal Casimir Force Betweenmentioning

confidence: 99%

Recent Results on Thermal Casimir Force Between Dielectrics and Related Problems

Geyer

Klimchitskaya

Mostepanenko

2006

Int. J. Mod. Phys. A

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“…It is also important that this force can be well controlled by specific shapes of corrugations (Blagov et al, 2004). Based on the path integral theory (Emig et al, 2003) it appears that the lateral Casimir force is a promising venue for the demonstration of shape dependences and diffraction-like effects.…”

Section: Lateral Casimir Force and Casimir Torques A Lateral Camentioning

confidence: 99%

The Casimir force between real materials: Experiment and theory

2009

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“…There PFA can also be invalid, but this leads only to small corrections of the dominant normal Casimir force, which do not seem accessible experimentally at the moment. The lateral component of the Casimir force has recently been measured and analyzed within the PFA [10,11]. We find for experimentally realizable parameters that PFA overestimates the force by as much as 30%, which should allow for a rapid experimental check of its validity.…”

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confidence: 99%

Lateral Casimir Force beyond the Proximity-Force Approximation

Rodrigues¹,

Neto²,

et al. 2006

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We argue that the appropriate variable to study a non trivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the Proximity Force Approximation (PFA). The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the Proximity Force Approximation overestimates the force by up to 30%.Considerable experimental progress has been achieved [1] in the measurement of the Casimir force, opening the way for various applications in nano-science [2], particularly in the development of nano-or micro-electromechanical systems (NEMS or MEMS). Calculations are much simpler in the original Casimir geometry of two plane plates [3] which obeys a symmetry with respect to lateral translations and thus allows to derive the expression of the Casimir force from the reflection amplitudes which describe specular scattering on the plates [4].More general geometries open a far richer physics with a variety of extremely interesting theoretical predictions [5]. Up to now the experimental studies of the effect of geometry have been restricted to simple configurations which can be calculated with the help of the Proximity Force Approximation (PFA). This approximation is essentially equivalent to an averaging over plane-plane geometries and its result can be deduced from the force known in this geometry [6]. For example, it allows to evaluate the force between a plane and a sphere [7] provided the radius R of the sphere is much larger than the mirror separation R ≫ L. It is also valid for the description of the effect of roughness when the wavelengths associated with the plate deformations are large enough [8]. However PFA relies heavily on assuming some additivity of Casimir forces which is known to be generally not valid except for very smooth geometrical perturbations [9].The aim of the present paper is to study a configuration allowing a new test of QED theoretical predictions outside the PFA domain and independent of those already performed in the plane-plane geometry. The idea is to look for the lateral component of the Casimir force which appears, besides the usual normal component, when periodic corrugations with the same period are imprinted on the two metallic plates. This configuration contrasts with other ones, for example the normal Casimir force in the plane-sphere geometry or roughness corrections to it. There PFA can also be invalid, but this leads only to small corrections of the dominant normal Casimir force, which do not seem accessible experimentally at the moment. The lateral component of the Casimir force has recently been measured and analyzed within the PFA [10,11]. We find for experimentally realizable parameters that PFA overestimates the force by as much as 30%, which should allow for a ...

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Control of the lateral Casimir force between corrugated surfaces

Cited by 39 publications

References 35 publications

Recent Results on Thermal Casimir Force Between Dielectrics and Related Problems

Recent Results on Thermal Casimir Force Between Dielectrics and Related Problems

The Casimir force between real materials: Experiment and theory

Lateral Casimir Force beyond the Proximity-Force Approximation

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