Null energy condition violation: Tunneling versus the Casimir effect
Open accessAbstract
We show that tunneling between two degenerate minima, as allowed in a finite volume, leads to a nonextensive symmetric ground state. This results in a null energy condition violation for sufficiently low temperatures, when a continuous set of momenta in the box containing the field is assumed. Taking into account discrete momenta can modify this picture and is achieved via the addition of the Casimir energy to the tunneling-induced ground state energy. Focusing on zero-temperature, these nontrivial effects are found to compete, depending on the typical length scales involved.
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In Refs. [13, 21], the instanton contribution to the ground state energy is calculated by only keeping homogeneous fluctuations.
“In Refs. [13, 21], the instanton contribution to the ground state energy is calculated by only keeping homogeneous fluctuations.”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
Section IV (page unavailable) says the one-loop corrections from instanton jumps do not depend on momentum, supporting the claim about the jump contribution. But Appendix A (page unavailable) calculates fluctuations around the static saddle points using a three-dimensional momentum integral, and Appendix B includes those fluctuation factors in the instanton-pair contribution. Thus the full calculation does not keep only homogeneous fluctuations. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe prior result on the convex effective potential was obtained by neglecting the spatially inhomogeneous fluctuations around the instanton configuration, as well as the Casimir effect.
“This result was obtained by neglecting the spatially inhomogeneous fluctuations around the instanton configuration, as well as the Casimir effect.”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
Section IV (page unavailable) says the earlier calculation ignored momentum quantisation and therefore omitted the Casimir contribution, which was added later. The paper does not clearly say that the convex-potential result was obtained by neglecting spatially inhomogeneous fluctuations around instantons; it says one-loop corrections from instanton jumps do not depend on momentum. (LLM, conf=0.78)
Experimental — accuracy not yet measuredThe effective theory taking into account tunnelling of a real scalar field between two degenerate vacua has a convex effective potential, with a symmetric true vacuum at expectation value zero and a corresponding ground state energy lower than the original degenerate vacua.
“It was found that the effective potential is indeed convex, with a symmetric true vacuum at ⟨ ϕ ⟩ = 0 and a corresponding ground state energy lower than the original degenerate vacua, similarly to what happens in Quantum Mechanics.”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
NEC violation is known in the case of the Casimir effect and has been shown for tunnelling between degenerate vacua.
“An important feature related to the above finite-volume effects is the violation of the Null Energy Condition (NEC - see [18, 19] for reviews), which is known in the case of the Casimir effect, and which has been shown in [12, 13] for tunnelling between degenerate vacua.”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
The scalar field can tunnel between the two degenerate bare minima ±v, resulting in an effective theory with a symmetric vacuum state located at expectation value zero.
“As discussed in the Introduction, in this context the scalar field can tunnel between the two degenerate bare minima ± v , resulting in an effective theory with a symmetric vacuum state located at ⟨ ϕ ⟩ = 0 (see Figure 1).”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
The explicit effective potential has been calculated at quadratic order in prior work, where one finds a positive mass term, therefore showing convexity.
“The explicit effective potential has been calculated at quadratic order in [12, 13], where one finds a positive mass term, therefore showing convexity.”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
The result of Refs. [13, 21] can be obtained from Eq. (4.29) by neglecting the contributions from n = 0 fluctuations.
“This can be obtained from the result in Eq. (4.29) by neglecting the contributions from n = 0 fl uctuations, namely”
From Double-well instantons in finite volume (2024) · cites this paper as [13]
Appendix A separates an n=0 temperature-independent term from a sum over n≥1, but it does not say that the cited result is obtained by neglecting n=0 fluctuations. I searched for Eq. (4.29) and for a derivation that drops those fluctuations; neither appears in our copy of this paper. (LLM, conf=0.72)
Experimental — accuracy not yet measured
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Cites
Energy conditions in general relativity and quantum field theory
Kontou, E.-A., & Sanders, K. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab8fcf · Cited by 223 · see citing works
Convexity, gauge-dependence and tunneling rates
Plascencia, A. D., & Tamarit, C. (2016) · Journal of High Energy Physics · doi:10.1007/jhep10(2016)099 · Cited by 64 · see citing works
Symmetry restoration, tunneling, and the null energy condition
Alexandre, J., & Polonyi, J. (2022) · Physical Review D · doi:10.1103/physrevd.106.065008 · Cited by 8 · see citing works
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Cited by
Sorted by citations
Double-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
Self-citation
- Authors
- Alexandre, J., & Backhouse, D.
- Affiliations
- King's College London (GB)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2023-04-28
- Volume
- 107
- Issue
- 8
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W4367312519
- Cited by
- 6
- References
- 3
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 1
- FWCI
- 0.70
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical review. D/Physical review. D. (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- Research Portal (King's College London) (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- Leverhulme Trust (RPG-2021-299)
- Science and Technology Facilities Council (STFC-ST/T000759/1)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- null energy condition violation, quantum tunneling, degenerate minima, Casimir effect, Casimir energy, energy-momentum tensor
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