Proposed fitting function for the critical Casimir force on 4He film below the point

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.

Download Full-text

Unifying Theory for Casimir Forces: Bulk and Surface Formulations

Universe ◽

10.3390/universe7070225 ◽

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.

Download Full-text

Coupled effects of surface interaction and damping on electromechanical stability of functionally graded nanotubes reinforced torsional micromirror actuator

The Journal of Strain Analysis for Engineering Design ◽

10.1177/03093247211036826 ◽

2021 ◽

pp. 030932472110368

Author(s):

Weidong Yang ◽

Menglong Liu ◽

Linwei Ying ◽

Xi Wang

Keyword(s):

Casimir Force ◽

Volume Fraction ◽

Nonlocal Parameter ◽

Saddle Points ◽

Functionally Graded ◽

Heteroclinic Orbits ◽

Phase Portraits ◽

Squeeze Film ◽

Squeeze Film Damping ◽

Tilting Angle

This paper demonstrated the coupled surface effects of thermal Casimir force and squeeze film damping (SFD) on size-dependent electromechanical stability and bifurcation of torsion micromirror actuator. The governing equations of micromirror system are derived, and the pull-in voltage and critical tilting angle are obtained. Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC). A finite element analysis (FEA) model is established on the COMSOL Multiphysics platform, and the simulation of the effect of thermal Casimir force on pull-in instability is utilized to verify the present analytical model. The results indicate that the numerical results well agree with the theoretical results in this work and experimental data in the literature. Further, the influences of volume fraction and geometrical distribution of CNTs, thermal Casimir force, nonlocal parameter, and squeeze film damping on electrically actuated instability and free-standing behavior are detailedly discussed. Besides, the evolution of equilibrium states of micromirror system is investigated, and bifurcation diagrams and phase portraits including the periodic, homoclinic, and heteroclinic orbits are described as well. The results demonstrated that the amplitude of the tilting angle for FGX-CNTRC type micromirror attenuates slower than for FGO-CNTRC type, and the increment of CNTs volume ratio slows down the attenuation due to the stiffening effect. When considering squeeze film damping, the stable center point evolves into one focus point with homoclinic orbits, and the dynamic system maintains two unstable saddle points with the heteroclinic orbits due to the effect of thermal Casimir force.

Download Full-text

Casimir force on a light front

Progress in Particle and Nuclear Physics ◽

10.1016/j.ppnp.2020.103836 ◽

2020 ◽

pp. 103836

Author(s):

S.S. Chabysheva ◽

J.R. Hiller

Keyword(s):

Casimir Force ◽

Light Front

Download Full-text

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

International Journal of Modern Physics A ◽

10.1142/s0217751x02010145 ◽

2002 ◽

Vol 17 (06n07) ◽

pp. 798-803 ◽

Cited By ~ 7

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.

Download Full-text