Casimir effect for scalar fields under Robin boundary conditions on plates

Romeo, August; Saharian, A. A.

doi:10.1088/0305-4470/35/5/312

Cited by 189 publications

(315 citation statements)

References 34 publications

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“…This result (32) could also have been directly obtained by using the fact that, in the special case under consideration, the problem is conformally related to the corresponding one for Robin plates in Minkowski spacetime [15,16]. From this relation, it follows that…”

Section: Vacuum Expectation Value Of the Field Squaredmentioning

confidence: 67%

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Casimir effect for parallel plates in de Sitter spacetime

2010

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The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows to explicitly extract the contributions to the expectation values which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power-law (monotonic or oscillating), with independence of the value of the field mass.

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Section: Vacuum Expectation Value Of the Field Squaredmentioning

confidence: 67%

“…In the discussion below we will assume that all zeros are real. In particular, this is the case for the conditions b j 0 (see [15]). The positive solutions of Eq.…”

Section: Introductionmentioning

confidence: 92%

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Casimir effect for parallel plates in de Sitter spacetime

2010

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“…[27]). Hence, we conclude that the formulae given above for the core induced parts in the VEVs are valid in the case of the presence of bound states as well.…”

Section: Resultsmentioning

confidence: 99%

Vacuum polarization by a global monopole with finite core

Mello

Saharian

2006

J. High Energy Phys.

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We investigate the effects of a (D + 1)-dimensional global monopole core on the behavior of a quantum massive scalar field with general curvature coupling parameter. In the general case of the spherically symmetric static core, formulae are derived for the Wightman function, for the vacuum expectation values of the field square and the energy-momentum tensor in the exterior region. These expectation values are presented as the sum of point-like global monopole part and the core induced one. The asymptotic behavior of the core induced vacuum densities is investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. In particular, in the latter case we show that the behavior of the vacuum densities is drastically different for minimally and non-minimally coupled fields. As an application of general results the flowerpot model for the monopole's core is considered and the expectation values inside the core are evaluated.

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“…(1) (with the appropriate change of its parameters) and the BC from Eq. (2) describe the processes in acoustics [2], electrodynamics [3], plasma [4], scalar field theory [5][6][7][8], superconductivity [9][10][11][12] where the coefficient Λ is called the de Gennes distance [13], and others [14,15]. Nonexhaustive list of the relevant research efforts can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field E applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position Sx and momentum S k quantum information entropies and their Fisher information Ix and I k and Onicescu information energies Ox and O k counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, Λ = 0 (Neumann, Λ = ∞), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum Sx + S k . Analogously, at Λ = 0 and Λ = ∞ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as E 2/3 (E 1/3 ) and its inverse, respectively, leading to the field-independent product IxI k (OxO k ). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

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Casimir effect for scalar fields under Robin boundary conditions on plates

Cited by 189 publications

References 34 publications

Casimir effect for parallel plates in de Sitter spacetime

Casimir effect for parallel plates in de Sitter spacetime

Vacuum polarization by a global monopole with finite core

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

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