Advances in the Casimir Effect

Bordag, M.; Klimchitskaya, G. L.; Mohideen, U.; Mostepanenko, V. M.

doi:10.1093/acprof:oso/9780199238743.001.0001

Cited by 1,216 publications

(2,359 citation statements)

References 587 publications

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“…It has important implications on all scales, from mesoscopic condensed matter physics to cosmology. Since the original research by Casimir [24], for the electromagnetic field in the geometry of two parallel conducting plates, many theoretical and experimental works have been done in this direction (for reviews see [25][26][27][28][29][30]). In braneworlds, the boundary conditions imposed on the bulk fields will give…”

Section: Jhep11(2015)092mentioning

confidence: 99%

Vacuum currents in braneworlds on AdS bulk with compact dimensions

Bellucci

Saharian

Vardanyan

2015

J. High Energ. Phys.

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Abstract:The two-point function and the vacuum expectation value (VEV) of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on the background of AdS spacetime with partial toroidal compactification. The presence of a gauge field flux, enclosed by compact dimensions, is assumed. On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed. There is a range in the space of the values for the coefficient in the boundary condition where the Poincaré vacuum is unstable. This range depends on the location of the brane and is different for the regions between the brane and AdS boundary and between the brane and the horizon. In models with compact dimensions the stability condition is less restrictive than that for the AdS bulk with trivial topology. The vacuum charge density and the components of the current along non-compact dimensions vanish. The VEV of the current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It is decomposed into the boundary-free and brane-induced contributions. The asymptotic behavior of the latter is investigated near the brane, near the AdS boundary and near the horizon. It is shown that, in contrast to the VEVs of the field squared and energy-momentum tensor, the current density is finite on the brane and vanishes for the special case of Dirichlet boundary condition. Both the boundary-free and brane-induced contributions vanish on the AdS boundary. The brane-induced contribution vanishes on the horizon and for points near the horizon the current is dominated by the boundary-free part. In the near-horizon limit, the latter is connected to the corresponding quantity for a massless field in the Minkowski bulk by a simple conformal relation. Depending on the value of the Robin coefficient, the presence of the brane can either increase or decrease the JHEP11 (2015)092 vacuum currents. Applications are given for a higher-dimensional version of the RandallSundrum 1-brane model.

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Section: Jhep11(2015)092mentioning

confidence: 99%

Vacuum currents in braneworlds on AdS bulk with compact dimensions

Bellucci

Saharian

Vardanyan

2015

J. High Energ. Phys.

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“…As discussed in Eq. (19), from a given distance between sphere and plate, the points of the sphere nearer to the plate tends to increase the Casimir energy (giving a repulsive contribution), while the rest of points 2 (ωR/c) 3 (full curves) and PSA (points) at zero temperature for TI infinity plates with θ1 = −θ2 = π and different (0) as a function of the dimensionless distanced [7]. PSA tends to overestimate the absolute value of the energy, but captures the equilibrium distance without appreciable error.…”

Section: Casimir Energy Between Spheres and Platesmentioning

confidence: 99%

Casimir repulsion between topological insulators in the diluted regime

Rodriguez-López

2011

Phys. Rev. B

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The Pairwise Summation Approximation (PSA) of Casimir energy is applied to a system of two dielectrics with magnetoelectric coupling. In particular, the case of Topological Insulators (TI) is studied in detail. Depending on the the optical response of the TI, we obtain a stable equilibrium distance, atraction for all distances, or repulsion for all distances at zero temperature. This equilibrium distance disappears in the high temperature limit. These results are independent on the geometry of the TI, but are only valid in the diluted approximation.

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“…In 1948 Casimir [1] and Casimir and Polder [2], while presenting their work on the forces on neutral atoms and conducting plates, laid the foundations of what is now called the Casimir effect (for a review on the subject see for example [3]). The Casimir effect arises from the change in the zeropoint energy of the system [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

2014

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We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and the strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs show considerable sensitivity to the fine details of the shape of the background field which cannot be seen from the graph of the total Casimir energy. Finally, we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.

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Advances in the Casimir Effect

Cited by 1,216 publications

References 587 publications

Vacuum currents in braneworlds on AdS bulk with compact dimensions

Vacuum currents in braneworlds on AdS bulk with compact dimensions

Casimir repulsion between topological insulators in the diluted regime

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

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