- Access by Xinjiang University
Effective trace framework for self-similar Casimir systems
Phys. Rev. D 113, 125013 – Published 15 June, 2026
DOI: https://doi.org/10.1103/3x5c-4dyg
Abstract
The interaction of quantum fields with fractal and self-similar geometries encompasses multiple distinct physical regimes, including spectral geometry on intrinsic fractals, macroscopic self-similar Casimir configurations, and bounded Euclidean cavities with fractal boundaries. While the thermal equations of state and spectral asymptotics for these systems are well established, a cohesive treatment of the vacuum trace frequently conflates rigorous mathematical bounds with phenomenological models. In this manuscript, we systematically decouple these regimes and advance a unified effective framework combining the rigorous thermal trace of fractal radiation with a zero-temperature integrated vacuum trace for platelike self-similar geometries. We demonstrate that for systems governed by a scale-dependent Casimir coefficient , the anisotropic stress-energy tensor produces an integrated vacuum trace proportional to its logarithmic running, . We strictly differentiate this effective macroscopic backreaction from first-principles local trace anomalies on genuine fractal boundaries. Finally, we analyze finite-level () prefractal realizations, establishing the analytical prerequisites necessary to transition this effective formalism into a quantitatively predictive electromagnetic theory amenable to experimental verification.
Physics Subject Headings (PhySH)
Article Text
References (18)
- H. B. G. Casimir, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 51, 793 (1948).
- E. Akkermans, G. V. Dunne, and A. Teplyaev, Phys. Rev. Lett. 105, 230407 (2010).
- J. Kigami, Analysis on Fractals (Cambridge University Press, Cambridge, England, 2001).
- N. Kajino, J. Funct. Anal. 258, 1310 (2010).
- K. V. Shajesh, I. Brevik, I. Cavero-Peláez, and P. Parashar, Phys. Rev. D 94, 065003 (2016).
- K. V. Shajesh, P. Parashar, I. Cavero-Peláez, J. Kocik, and I. Brevik, Phys. Rev. D 96, 105010 (2017).
- S. Alexander and R. Orbach, J. Phys. Lett. 43, 625 (1982).
- L. S. Brown and G. J. Maclay, Phys. Rev. 184, 1272 (1969).
- M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford, 2009).
- O. Kenneth and I. Klich, Phys. Rev. Lett. 97, 160401 (2006).
- M. L. Lapidus, Trans. Am. Math. Soc. 325, 465 (1991).
- L. S. Brown and J. P. Cassidy, Phys. Rev. D 16, 1712 (1977).
- N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
- C. P. Herzog and K.-W. Huang, Phys. Rev. D 87, 081901 (2013).
- K. A. Milton, S. A. Fulling, P. Parashar, P. Kalauni, and T. Murphy, Phys. Rev. D 93, 085017 (2016).
- K. A. Milton, J. Phys. A 37, 6391 (2004).
- A. W. Rodriguez, F. Capasso, and S. G. Johnson, Nat. Photonics 5, 211 (2011).
- S. Avino, E. Calloni, S. Caprara, M. De Laurentis, R. De Rosa, T. Di Girolamo, L. Errico, G. Gagliardi, M. Grilli, V. Mangano et al., Physics (Amsterdam) 2, 1 (2020).
