Casimir effect between ponderable media as modeled by the standard model extension

Martín-Ruiz, A.; Escobar, C. A.

doi:10.1103/physrevd.94.076010

Cited by 46 publications

(40 citation statements)

References 90 publications

(54 reference statements)

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“…This analysis is consistent with the electromagnetic fields computed in Refs. [24][25][26] for different simple sources. In the problem at hand, the source of the electromagnetic fields is the constant potential V 0 at the surface of the sphere.…”

Section: B Recurrence Equationsmentioning

confidence: 99%

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Magnetoelectric effect of a conducting sphere near a planar topological insulator

et al. 2019

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When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular bispherical coordinate system. We find that the electromagnetic fields can be interpreted in terms of point electric and image magnetic charges as if the medium were the vacuum. As a manifestation of the magnetoelectric effect, we highlight the resulting magnetic field, which we analyze in detail along the symmetry axis, since such estimates could be useful in evaluating the experimental possibility of its measurement via sensible magnetometers. Our numerical estimates show that the proposed setup provides a magnetic field strength in the range of 10-100 mG, which is attainable with present day sensitivities in NV center-diamond magnetometers, for example. I. INTRODUCTIONGeneral magnetoelectric (ME) media are characterized by additional relations between the magnetic (electric) field and the polarization (magnetization), aside from the standard connection found in conventional dielectrics [1][2][3][4]. A linear ME material is described by the ME term θ ij E i B j in the free enthalpy of the system, where θ ij is the ME tensor which can be either symmetric or antisymmetric [5]. In the simplest case, when θ ij = θδ ij , we recover the ME coupling θ E · B, which we recognize as that of axion electrodynamics, with θ being the axion field [6]. In the context of particle physics, the axion is an additional pseudoscalar degree of freedom which gives a solution to the strong CP problem [7]. Linear magnetoelectrics can be realized in topological materials, such as topological insulators (TIs) [8][9][10][11] and Weyl semimetals (WSMs) [12].Topological phases are an emerging class of materials which have attracted much attention in condensed matter physics. Among them, the most studied are the TIs, which are time-reversal-symmetric materials characterized by a fully insulating bulk with protected conducting surface states [9,10]. This behavior was first predicted in two-dimensional HgTe/CdTe quantum wells [13][14][15] and less than one year after, it was experimentally observed [16]. The generalization to three-dimensional compounds came shortly afterwards [17][18][19]. In particular, Fu and Kane [20] predicted that the alloy Bi 1−x Sb x would be a three-dimensional (3D) TI in a special range of x, and it was experimentally confirmed one year later [21]. A second generation of 3D TIs was predicted to occur in the stoichiometric crystals Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 [22], and they were experimentally discovered in 2009 [22,23]...

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Section: B Recurrence Equationsmentioning

confidence: 99%

“…For an extensive review of the electromagnetic response of 3D TIs, see Refs. [24][25][26]. In the following, we briefly survey some alternatives that have been proposed to determine the quantized behavior of the ME effect, codified in the integer values that θ can take.…”

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Magnetoelectric effect of a conducting sphere near a planar topological insulator

et al. 2019

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“…Possible effects of Lorentz symmetry violation have been investigated in many contexts, for example, the Casimir effect [8][9][10][11], QED [12][13][14][15][16], hydrogen atom [17,18], noncommutative field theories [19][20][21], space-times with a non-trivial topology [22], gravity theory [23][24][25][26][27][28], electromagnetic wave propagation [29][30][31][32], studies of photon field quantization [33][34][35], effects on the classical electrodynamics [36][37][38][39][40][41], among others.…”

Section: Introductionmentioning

confidence: 99%

A perfectly conducting surface in electrodynamics with Lorentz symmetry breaking

Borges

Barone

2017

Eur. Phys. J. C

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In this paper we consider a model which exhibits explicit Lorentz symmetry breaking due to the presence of a single background vector v μ coupled to the gauge field. We investigate such a theory in the vicinity of a perfectly conducting plate for different configurations of v μ . First we consider no restrictions on the components of the background vector and we treat it perturbatively up to second order. Next, we treat v μ exactly for two special cases: the first one is when it has only components parallel to the plate, and the second one when it has a single component perpendicular to the plate. For all these configurations, the propagator for the gauge field and the interaction force between the plate and a point-like electric charge are computed. Surprisingly, it is shown that the image method is valid in our model and we argue that it is a non-trivial result. We show there arises a torque on the mirror with respect to its positioning in the background field when it interacts with a point-like charge. It is a new effect with no counterpart in theories with Lorentz symmetry in the presence of a perfect mirror.

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“…where D is the rectangular domain defined in Eq. (23). The calculation proceeds just as in the massless case: we first introduce the Schwinger proper time representation for the square root and integrate x.…”

Section: B Massive Casementioning

confidence: 99%

Casimir effect in polymer scalar field theory

2020

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In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance L, due to the presence of a minimal length λ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming λ L, we expressed it as an expansion in powers of 1/N , being N = L/λ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

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Casimir effect between ponderable media as modeled by the standard model extension

Cited by 46 publications

References 90 publications

Magnetoelectric effect of a conducting sphere near a planar topological insulator

Magnetoelectric effect of a conducting sphere near a planar topological insulator

A perfectly conducting surface in electrodynamics with Lorentz symmetry breaking

Casimir effect in polymer scalar field theory

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