Theoretical analysis of Casimir and thermal Casimir effect in stationary space–time

Zhang, Anwei

doi:10.1016/j.physletb.2017.08.012

Cited by 12 publications

(21 citation statements)

References 18 publications

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“…Our goal is to analyze the impact of scalar field mass and the apparatus orientation with respect to the symmetry axis, x 1 , on the Casimir energy. We also compare our results with previous ones, where a specific orientation was chosen for the massless field case [13,14]. Since energy is a frame-dependent quantity, we must choose the same coordinate frame used in these papers.…”

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 78%

“…At a first glance, the constant metric approximation on the Klein-Gordon equation makes the problem appear equivalent to the flat case. However, it has been demonstrated by Sorge [13] and Zhang [14] that this situation is not equivalent to the one in flat space-time. As pointed out in [13], this unexpected behavior is due to a symmetry breaking.…”

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 97%

“…We call D the KG operator. Now, we assume the same approximation made in [13,14]. Namely, that the apparatus has a small size compared to the scale on which the metric varies.…”

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 99%

“…Namely, for a Casimir apparatus in an axial symmetric metric, with non-diagonal element g t x and the plates orthogonal to the x-direction, the associated break of translational invariance induces a distortion in the discretized field modes inside the cavity. In [14] it is shown that, even in this constant metric approximation, the breaking of translational invariance induces non-trivial corrections in Casimir thermodynamic description. For more developments and discussion in this context see [19,20].…”

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 99%

“…In the aforementioned work, the plates of the apparatus are oriented parallel to the radial coordinate of the gravitational source. The extension for a general stationary spacetime was presented in [14].…”

Section: Introductionmentioning

confidence: 99%

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Repulsive Casimir force in stationary axisymmetric spacetimes

et al. 2022

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We study the influence of stationary axisymmetric spacetimes on Casimir energy. We consider a massive scalar field and analyze its dependence on the apparatus orientation with respect to the dragging direction associated with such spaces. We show that, for an apparatus orientation not considered before in the literature, the Casimir energy can change its sign, producing a repulsive force. As applications, we analyze two specific metrics: one associated with a linear motion of a cylinder and a circular equatorial motion around a gravitational source described by Kerr geometry.

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Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 78%

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 97%

“…We call D the KG operator. Now, we assume the same approximation made in [13,14]. Namely, that the apparatus has a small size compared to the scale on which the metric varies.…”

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 99%

Section: Klein-gordon Equation and The Frequenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Repulsive Casimir force in stationary axisymmetric spacetimes

et al. 2022

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Casimir effect in conformally flat spacetimes

Markowicz

Dębski

Kolanowski

et al. 2020

Class. Quantum Grav.

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We discuss several approaches to determine the Casimir force in inertial frames of reference in different dimensions. On an example of a simple model involving mirrors in Rindler spacetime we show that Casimir’s and Lifschitz’s methods are inequivalent and only the latter provides the correct force in other spacetime geometries. For conformally coupled fields we derive the Casimir force in conformally flat spacetimes utilizing an anomaly and provide explicit examples in the Friedmann–Lemaître–Robertson–Walker (k = 0) models.

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Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror

et al. 2023

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In this paper we study the propagation of structured optical scalar beams in a Lorentz-violating (LV) vacuum parametrized by a constant 4-vector $u^{\mu}$ and in the presence of a semi-transparent mirror. The two bosonic degrees of freedom of the electromagnetic field can be described by a LV extension of the massless scalar field theory, whose LV part is characterized by the term $(u \cdot \partial \phi ) ^{2}$. The mirror at a surface $\Sigma$ is modelled by a delta-type potential in the Lagrange density for the LV scalar field, i.e. $\lambda \delta (\Sigma ) \phi ^{2}$, where the parameter $\lambda$ controls the degree of transparency of the mirror. Using Green's function techniques, we investigate the propagation of a Gaussian beam in the presence of a mirror which is perpendicular to the propagation direction and for two particular choices of the background 4-vector: parallel and perpendicular to the propagation direction. To quantify the Lorentz-violating effects we introduce the fidelity as a measurement of the closeness of the propagated field distribution with respect to that in the conventional vacuum. In the absence of the mirror ($\lambda = 0$) the fidelity is found to be close to one, and hence LV effects are quite small. However in the presence of the mirror, there are regions where the fidelity drops to zero, thus implying that LV effects could be clearly differentiated from the propagation in vacuum. Within the paraxial approximation we determine analytically the LV effects upon the Rayleigh range, the radius of the beam, the Gouy phase and the radius of curvature of the wavefronts. We discuss possible scenarios where our results could apply, by using optically transparent multiferroic materials, which offer unprecedented opportunities to tailor structured beam propagation, as well as to simulate an LV vacuum.

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Theoretical analysis of Casimir and thermal Casimir effect in stationary space–time

Cited by 12 publications

References 18 publications

Repulsive Casimir force in stationary axisymmetric spacetimes

Repulsive Casimir force in stationary axisymmetric spacetimes

Casimir effect in conformally flat spacetimes

Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror

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