The Casimir effect: Some aspects

Brazilian Journal of Physics (Impact Factor: 0.81). 01/2007; 36(4). DOI: 10.1590/S0103-97332006000700006
Source: arXiv


We start this paper with a historical survey of the Casimir effect, showing that its origin is related to experiments on colloidal chemistry. We present two methods of computing Casimir forces, namely: the global method introduced by Casimir, based on the idea of zero-point energy of the quantum electromagnetic field, and a local one, which requires the computation of the energy-momentum stress tensor of the corresponding field. As explicit examples, we calculate the (standard) Casimir forces between two parallel and perfectly conducting plates and discuss the more involved problem of a scalar field submitted to Robin boundary conditions at two parallel plates. A few comments are made about recent experiments that undoubtedly confirm the existence of this effect. Finally, we briefly discuss a few topics which are either elaborations of the Casimir effect or topics that are related in some way to this effect as, for example, the influence of a magnetic field on the Casimir effect of charged fields, magnetic properties of a confined vacuum and radiation reaction forces on non-relativistic moving boundaries.

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    • "The Casimir effect was mentioned and presented theoretically in 1948 for the first time by the Dutch physicist Hendrik Brugt Gerhard Casimir (1909–2000), who investigates the attraction of two parallel plates in the vacuum [9]. Several researches investigated the role of the Casimir effect on the pull-in phenomenon in N/MEMS [10] [11] [12] [13]. "
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    ABSTRACT: The objective of the present paper is to represent a novel method to investigate the stable and unstable behaviors of fully clamped rectangular nano/microplates under the effects of electrostatic and Casimir pressures. To this end, the governing partial differential equation of equilibrium is considered and reduced to an algebraic equation using a simple and computationally efficient single degree of freedom (SDOF) model through the Galerkin weighted residual method. The linear and undamped mode-shapes of the plate are used in the Galerkin procedure as the weight function which is obtained by the extended Kantorovich method (EKM). The present findings are compared and validated by available empirical and theoretical results in the literature as well as those obtained by finite element (FE) simulation carried out using COMSOL Multiphysics commercial software and excellent agreements between them are observed.
    Full-text · Article · Feb 2015
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    • "The case of a 3D cavity with conducting and permeable oscillating plates (described by means of the Dirichlet and Neumann boundary conditions) was studied in [44] [45]. The Robin boundary conditions in 1+1 dimensions were considered in [46] [47]. The one-dimensional cavity with one and two oscillating mirrors was considered within the framework of the 'optical' approach in [48]. "
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    ABSTRACT: This is a brief description of some recent achievements in the theory of dynamical Casimir effect, mainly in connection with the experiment which is under preparation in the University of Padua. The first part of this paper is devoted to the theory of quantum damped oscillator with arbitrary time dependence of the frequency and damping coefficient. New results for the mean number of created photons, its variance and photon distribution function are given. The second part is devoted to calculations of the time-dependent shift of resonance frequency of an electromagnetic cavity due to strong variations of dielectric properties in a thin layer near an ideally conducting wall. A simple analytical formula for this shift is derived. It generalizes the known Schwinger-Bethe-Casimir result. The influence of different parameters on the photon generation rate is discussed. A brief review of recent publications on the subject is also included.
    Full-text · Article · Apr 2009 · Journal of Physics Conference Series
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    ABSTRACT: This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed. Comment: 31 pages
    Full-text · Article · Apr 2008 · Journal of Mathematical Physics
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