Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons

Abstract

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a $(D+1)$-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.

21 pages, 4 figures

References in corpus (30)

• Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates
• Opposites Attract - A Theorem About The Casimir Force
• Casimir force on a piston
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
• Casimir interaction of two plates inside a cylinder
• Casimir piston for massless scalar fields in three dimensions
• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Comment on the sign of the Casimir force
• Dark Energy and Stabilization of Extra Dimensions
• Casimir pistons with hybrid boundary conditions
• Kaluza-Klein models as pistons
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• The Casimir Force in Randall Sundrum Models
• Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model
• Casimir force for a scalar field in warped brane worlds
• The Casimir Force in Randall Sundrum Models with q+1 dimensions
• The Casimir force on a piston in the spacetime with extra compactified dimensions
• The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Compact dimensions and the Casimir effect: the Proca connection
• Comment on: "The Casimir force on a piston in the spacetime with extra compactified dimensions" [Phys. Lett. B 668 (2008) 72]
• The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions
• Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Estimative for the size of the compactification radius of a one extra dimension Universe
• Dark energy and moduli stabilization of extra dimensions in M^{1+3}xT^2 spacetime
• Casimir effect with non-local boundary conditions

Cited by in corpus (74)

• Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• Casimir effect for parallel plates in de Sitter spacetime
• Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• A simple model for the dynamical Casimir effect for a static mirror with time-dependent properties
• Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models
• Topological Casimir effect in compactified cosmic string spacetime
• Finite temperature Casimir effect for charged massless scalars in a magnetic field
• Casimir effect of electromagnetic field in Randall-Sundrum spacetime
• Casimir Effect in the Kerr Spacetime with Quintessence
• Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
• Finite Temperature Casimir Effect in Randall-Sundrum Models
• Casimir force in brane worlds: coinciding results from Green's and Zeta function approaches
• Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches
• Casimir effect for parallel metallic plates in cosmic string spacetime
• Casimir Effect on the brane
• 3D scalar model as a 4D perfect conductor limit: dimensional reduction and variational boundary conditions
• Casimir Piston of Real Materials and its Application to Multi-Layer Models
• Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field
• Pistons modeled by potentials
• Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions
• Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions
• Casimir effect due to a slowly rotating source in the weak field approximation
• Casimir effect for scalar current densities in topologically nontrivial spaces
• Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field
• Null Second Order Corrections to Casimir Energy in Weak Gravitational Field
• Slab Bag Fermionic Casimir effect, Chiral Boundaries and Vector Boson - Majorana Fermion Pistons
• Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures
• Repulsive Casimir Force from Fractional Neumann Boundary Conditions
• The Casimir effect for parallel plates involving massless Majorana fermions at finite temperature
• Vacuum densities for a brane intersecting the AdS boundary
• Casimir effect in de Sitter spacetime
• The Casimir effect for parallel plates in the spacetime with a fractal extra compactified dimension
• Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution
• Casimir Effect in the Presence of External Fields
• Quantum information measures of the one-dimensional Robin quantum well
• Casimir Pistons with General Boundary Conditions
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Electromagnetic two-point functions and the Casimir effect in Friedmann-Robertson-Walker cosmologies
• Electromagnetic Casimir piston in higher dimensional spacetimes
• Classification of the sign of the critical Casimir force in two dimensional systems at asymptotically large separations
• Spherical Casimir pistons
• Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
• Vacuum currents in partially compactified Rindler spacetime with an application to cylindrical black holes
• The Horava-Lifshitz Modifications of the Casimir effect at finite temperature revisted
• One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
• The Casimir Effect for Generalized Piston Geometries
• Null second order corrections to Casimir energy in weak gravitational field: The Schwinger's approach
• Revisiting Vacuum Energy in Compact Spacetimes
• Casimir energy of $N$ magnetodielectric $\delta$-function plates
• Horizon Complementarity and Casimir Violations of the Null Energy Condition
• Vacuum polarization with zero-range potentials on a hyperplane
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Kaluza-Klein Pistons with non-Commutative Extra Dimensions
• Perturbative approach to Dynamical Casimir effect in an interface of dielectric mediums
• The Casimir effect for parallel plates at finite temperature in the presence of one fractal extra compactified dimension
• Semitransparent pistons
• Finite Temperature Casimir Effect in the Presence of Extra Dimensions
• Casimir force for cosmological domain walls
• Quasi-local stress-tensor formalism and the Casimir effect
• Quantum vacuum under mixed boundary conditions: the case for curved spacetime
• Denouement of a Wormhole-Brane Encounter
• Radiation dominated era and the power of general relativity
• Vacuum instability in Kaluza-Klein manifolds
• The proximity force approximation for the Casimir energy of plate-sphere and sphere-sphere systems in the presence of one extra compactified universal dimension
• Spherical Casimir effect for a massive scalar field on the three dimensional ball
• Massive scalar Casimir interaction beyond proximity force approximation
• Decoupling Inflation From the String Scale
• Fermionic Casimir effect in the presence of compact dimension in field theory with Lorentz invariance violation
• The cosmological constant as an eigenvalue of a Sturm-Liouville problem