Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition

Abstract

In this work we consider the generalized zeta function method to obtain temperature corrections to the vacuum (Casimir) energy density, at zero temperature, associated with quantum vacuum fluctuations of a scalar field subjected to a helix boundary condition and whose modes propagate in (3+1)-dimensional Euclidean spacetime. We find closed and analytical expressions for both the two-point heat kernel function and free energy density in the massive and massless scalar field cases. In particular, for the massless scalar field case, we also calculate the thermodynamics quantities internal energy density and entropy density, with their corresponding high- and low-temperature limits. We show that the temperature correction term in the free energy density must suffer a finite renormalization, by subtracting the scalar thermal blackbody radiation contribution, in order to provide the correct classical limit at high temperatures. We check that, at low temperature, the entropy density vanishes as the temperature goes to zero, in accordance with the third law of thermodynamics. We also point out that, at low temperatures, the dominant term in the free energy and internal energy densities is the vacuum energy density at zero temperature. Finally, we also show that the pressure obeys an equation of state.

16 pages, new discussions and appendix added, to be published in PRD

References in corpus (11)

• The Casimir effect: from quantum to critical fluctuations
• Casimir force on a piston
• Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry
• Casimir piston for massless scalar fields in three dimensions
• Casimir Effect in the Rainbow Einstein's Universe
• Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Quantum Spring from the Casimir Effect
• Ultrastatic spacetimes
• Quantum vacuum fluctuation effects in a quasi-periodically identified conical spacetime
• Quantum Spring

Cited by in corpus (7)

• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Casimir effect, loop corrections and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions
• Thermal Casimir effect in the Einstein Universe with a spherical boundary
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Vacuum energy, temperature corrections and heat kernel coefficients in $(D+1)$-dimensional spacetimes with nontrivial topology
• Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions
• Topological Casimir effect in models with helical compact dimensions