scholarly journals Theory of Casimir Forces without the Proximity-Force Approximation

2016 ◽  
Vol 116 (11) ◽  
Author(s):  
Luciano C. Lapas ◽  
Agustín Pérez-Madrid ◽  
J. Miguel Rubí
Keyword(s):  
Casimir Forces ◽  
Proximity Force Approximation

scholarly journals Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mingkang Wang ◽  
L. Tang ◽  
C. Y. Ng ◽  
Riccardo Messina ◽  
Brahim Guizal ◽  
...  
Keyword(s):  
Casimir Force ◽  
Quantum Fluctuations ◽  
Complex Geometries ◽  
Casimir Forces ◽  
Recent Advances ◽  
Geometry Dependence ◽  
Proximity Force Approximation ◽  
On Chip

AbstractQuantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

Casimir forces and vacuum energy

2017 ◽  
Author(s):  
Serge Reynaud ◽  
Astrid Lambrecht
Keyword(s):  
Casimir Force ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Thermal Fluctuations ◽  
Model Systems ◽  
Vacuum Field ◽  
Force Measurements ◽  
Casimir Forces ◽  
Current State ◽  
Field Fluctuations

The Casimir force is an effect of quantum vacuum field fluctuations, with applications in many domains of physics. The ideal expression obtained by Casimir, valid for perfect plane mirrors at zero temperature, has to be modified to take into account the effects of the optical properties of mirrors, thermal fluctuations, and geometry. After a general introduction to the Casimir force and a description of the current state of the art for Casimir force measurements and their comparison with theory, this chapter presents pedagogical treatments of the main features of the theory of Casimir forces for one-dimensional model systems and for mirrors in three-dimensional space.

scholarly journals Measuring the Casimir Forces with an Adhered Cantilever: Analysis of Roughness and Background Effects

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 64
Author(s):  
Ivan A. Soldatenkov ◽  
Anastasiya A. Yakovenko ◽  
Vitaly B. Svetovoy
Keyword(s):  
Residual Stress ◽  
Surface Roughness ◽  
Short Distance ◽  
Technological Progress ◽  
Experimental Information ◽  
Casimir Forces ◽  
Raw Data ◽  
Micromechanical Devices ◽  
Negligible Contribution

Technological progress has made possible precise measurements of the Casimir forces at distances less than 100 nm. It has enabled stronger constraints on the non-Newtonian forces at short separations and improved control of micromechanical devices. Experimental information on the forces below 30 nm is sparse and not precise due to pull-in instability and surface roughness. Recently, a method of adhered cantilever was proposed to measure the forces at small distances, which does not suffer from the pull-in instability. Deviation of the cantilever from a classic shape carries information on the forces acting nearby the adhered end. We calculate the force between a flat cantilever and rough Au plate and demonstrate that the effect of roughness dominates when the bodies approach the contact. Short-distance repulsion operating at the contact is included in the analysis. Deviations from the classic shape due to residual stress, inhomogeneous thickness of the cantilever, and finite compliance of the substrate are analysed. It is found that a realistic residual stress gives a negligible contribution to the shape, while the finite compliance and inhomogeneous thickness give measurable contributions that have to be subtracted from the raw data.

scholarly journals Unifying Theory for Casimir Forces: Bulk and Surface Formulations

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 225
Author(s):  
Giuseppe Bimonte ◽  
Thorsten Emig
Keyword(s):  
Free Energy ◽  
Path Integral ◽  
Casimir Force ◽  
Hamiltonian Formulation ◽  
Current Fluctuations ◽  
Practical Application ◽  
Casimir Forces ◽  
Surface Approach ◽  
Maxwell Stress Tensor ◽  
Electromagnetic Fluctuation

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

scholarly journals Thermal Casimir effect with general boundary conditions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
L. Santamaría-Sanz ◽  
M. Donaire ◽  
M. Tello-Fraile
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Thermal Correction ◽  
Frequency Independent ◽  
Scalar Quantum

Abstract In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

scholarly journals Critical adsorption and critical Casimir forces for geometrically structured confinements

2008 ◽  
Vol 129 (12) ◽  
pp. 124716 ◽  
Author(s):  
M. Tröndle ◽  
L. Harnau ◽  
S. Dietrich
Keyword(s):  
Casimir Forces

Casimir forces

1992 ◽  
Vol 33 (5) ◽  
pp. 313-322 ◽  
Author(s):  
Peter W. Milonni ◽  
Mei-Li Shih
Keyword(s):  
Casimir Forces

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

Heat Transfer Spectroscopy and “Heat Transfer-Distance” Curves

2008 ◽  
Author(s):  
Arvind Narayanaswamy ◽  
Sheng Shen ◽  
Gang Chen
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Atomic Force Microscope ◽  
Near Field ◽  
Surface Force ◽  
Casimir Forces ◽  
Distance Curve ◽  
Transfer Distance ◽  
Atomic Force ◽  
Order Of Magnitude

Thermal radiative transfer between objects as well as near-field forces such as van der Waals or Casimir forces have their origins in the fluctuations of the electrodynamic field. Near-field radiative transfer between two objects can be enhanced by a few order of magnitude compared to the far-field radiative transfer that can be described by Planck’s theory of blackbody radiation and Kirchoff’s laws. Despite this common origin, experimental techniques of measuring near-field forces (using the surface force apparatus and the atomic force microscope) are more sophisticated than techniques of measuring near-field radiative transfer. In this work, we present an ultra-sensitive experimental technique of measuring near-field using a bi-material atomic force microscope cantilever as the thermal sensor. Just as measurements of near-field forces results in a “force distance curve”, measurement of near-field radiative transfer results in a “heat transfer-distance” curve. Results from the measurement of near-field radiative transfer will be presented.

Sign in / Sign up

Export Citation Format

Share Document