Attractive and Repulsive Casimir Vacuum Energy with General Boundary Conditions

Abstract

The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.

21 pages, 11 figures

References in corpus (15)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Casimir forces between arbitrary compact objects
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• The Casimir effect within scattering theory
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir Forces between Compact Objects: I. The Scalar Case
• Multiple Scattering Methods in Casimir Calculations
• Casimir Effect and Global Theory of Boundary Conditions
• Vacuum Boundary Effects
• Vacuum Energy and Renormalization on the Edge
• Models of Topology Change
• Constraints on non-Newtonian gravity and light elementary particles from measurements of the Casimir force by means of dynamic AFM
• Boundary Effects in Quantum Physics
• Quantum Physics and Fluctuating Topologies: Survey
• Vacuum Structure and Boundary Renormalization Group

Cited by in corpus (60)

• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• Fermionic Casimir effect in a field theory model with Lorentz symmetry violation
• QFT over the finite line. Heat kernel coefficients, spectral zeta functions and selfadjoint extensions
• Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model
• Casimir forces on deformed fermionic chains
• Edge States at Phase Boundaries and Their Stability
• Dirac lattices, zero-range potentials and self adjoint extension
• Self-adjoint extensions and unitary operators on the boundary
• Quantum vacuum interaction between two cosmic strings revisited
• Casimir effect for perfect electromagnetic conductors (PEMCs): A sum rule for attractive/repulsive forces
• Remarks on the Casimir force for magnetodielectric media
• Repulsive Casimir force in Bose-Einstein Condensate
• Beyond-proximity-force-approximation Casimir force between two spheres at finite temperature II: plasma versus Drude modeling, grounded versus isolated spheres
• Point interactions with bias potentials
• Casimir effect in Snyder Space
• Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states
• Vacuum energy for generalised Dirac combs at $T=0$
• Boundary Conditions as Dynamical Fields
• Casimir Pistons with General Boundary Conditions
• Thermal Casimir effect with general boundary conditions
• Quantum field theories with boundaries and novel instabilities
• The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity
• Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schrödinger operator in one dimension
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds
• Hyperspherical $\delta \text{-}{\delta }^{\prime }$ potentials
• Repulsive to Attractive Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model
• Fermionic edge states and new physics
• Switching the sign of the Casimir force between two PEMC spheres
• Scattering data and bound states of a squeezed double-layer structure
• Boundaries without boundaries
• Near-Dirichlet quantum dynamics for a $p^3$-corrected particle on an interval
• Boundary conditions for the quantum Hall effect
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Casimir Energy in (2 + 1)-Dimensional Field Theories
• Vacuum polarization with zero-range potentials on a hyperplane
• Modelling quantum black hole
• Repulsive Casimir-Lifshitz pressure in closed cavities
• One-dimensional scattering of fermions in double Dirac delta potentials
• Revisiting the Casimir Energy with General Boundary Conditions, and applications in 1D Crystals
• Energy preserving boundary conditions in field theory
• The Casimir effect for pistons with transmittal boundary conditions
• Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves
• Casimir pistons with generalized boundary conditions: a step forward
• Aspects of Boundary Conditions for Nonabelian Gauge Theories
• Electromagnetic vacuum densities induced by a cosmic string
• Casimir Wormholes in Brans-Dicke Theory
• Quantum magnetic billiards: boundary conditions and gauge transformations
• Quantum vacuum under mixed boundary conditions: the case for curved spacetime
• Casimir energy of hyperbolic orbifolds with conical singularities
• Scale limited fields and the Casimir effect
• The Casimir Effect for Thick Pistons
• Isospectrality and non-locality of generalized Dirac combs
• Casimir energy through transfer operators for sine-Gordon backgrounds
• Black holes and quantum theory on manifolds with singular potentials
• Quantum field theory at finite temperature for 3D periodic backgrounds
• Casimir energy for $N$ constant conductivity $\delta$-plates with a neural network perception