Chern-Simons boundary layers in the Casimir effect

Marachevsky, Valery N.

doi:10.1142/s0217732320400155

Cited by 6 publications

(5 citation statements)

References 49 publications

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“…References [32][33][34] have further examined this problem showing that the behavior shown in Equations ( 4) and ( 5) may be overtaken by making the longitudinal conductivity of the interacting materials more prominent or by considering shorter separations, for which the interaction is similar to the one for two regular dielectrics. In the case of dielectric substrates covered with Chern-Simons layers, however, a repulsive Casimir regime is observed at shorter separations, while at larger distances, the interaction resembles one of ordinary dielectrics [35,36]. The Casimir-Polder energy between an atom and a Chern-Simons surface may be repulsive or attractive depending on the sign of the Chern number [37].…”

Section: Nontrivial Topology In Materialsmentioning

confidence: 99%

Perspective on Some Recent and Future Developments in Casimir Interactions

2020

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Here, we present a critical review of recent developments in Casimir physics motivated by discoveries of novel materials. Specifically, topologically nontrivial properties of the graphene family, Chern and topological insulators, and Weyl semimetals have diverse manifestations in the distance dependence, presence of fundamental constants, magnitude, and sign of the Casimir interaction. Limited studies of the role of nonlinear optical properties in the interaction are also reviewed. We show that, since many new materials have greatly enhanced the nonlinear optical response, new efficient pathways for investigation of the characteristic regimes of the Casimir force need to be explored, which are expected to lead to new discoveries. Recent progress in the dynamical Casimir effect is also reviewed and we argue that nonlinear media can open up new directions in this field as well.

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Section: Nontrivial Topology In Materialsmentioning

confidence: 99%

Perspective on Some Recent and Future Developments in Casimir Interactions

2020

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“…Here, we prove the equivalence of the Casimir energy (86) to the result for the Casimir energy obtained with the scattering approach [43,44]. In the present paper, we use the local polar basis vectors e r and e φ in momentum space; in Ref.…”

Section: Appendix a Representations Of The Casimir Energy In Two Basesmentioning

confidence: 52%

“…It was demonstrated in Ref. [44] that for two SiO 2 substrate half-spaces separated by a vacuum slit, the Casimir repulsion can be realized at the maximum distance d = 26.52 nm between half-spaces; the maximum distance at which the Casimir repulsion occurs in this system corresponds to Chern-Simons constants a 1 = a 2 = 0.542 or m = n = 74. In Ref.…”

Section: Casimir Interaction In Systems With Chern-simons Layers On R...mentioning

confidence: 93%

“…The Casimir repulsion for two half-spaces covered by Chern-Simons layers was studied for Au, intrinsic Si and SiO 2 glass substrate materials in Refs. [43,44]. In Ref.…”

Section: Casimir Interaction In Systems With Chern-simons Layers On R...mentioning

confidence: 99%

“…In Ref. [44], it was shown that the minimum of the Casimir energy with d > 10 nm is achieved for integer m = n ∈ [34,115]. The Casimir interaction of Chern-Simons layers in the presence of realistic substrate materials was not studied for small enough and different values of a 1 and a 2 or for geometries different from two half-space substrates with boundary Chern-Simons layers.…”

Section: Casimir Interaction In Systems With Chern-simons Layers On R...mentioning

confidence: 99%

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Casimir Interaction of Chern–Simons Layers on Substrates via Vacuum Stress Tensor

Marachevsky,

Sidelnikov

2024

Physics

Self Cite

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We develop a Green’s functions scattering method for systems with Chern–Simons plane boundary layers on dielectric half-spaces. The Casimir pressure is derived by evaluation of the stress tensor in a vacuum slit between two half-spaces. The sign of the Casimir pressure on a Chern–Simons plane layer separated by a vacuum slit from the Chern–Simons layer at the boundary of a dielectric half-space is analyzed for intrinsic Si and SiO2 glass substrates.

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Nonlinear actuation of micromechanical Casimir oscillators with topological insulator materials toward chaotic motion: Sensitivity on magnetization and dielectric properties

Tajik

Allameh

Masoudi

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We have investigated the dynamical actuation of micro-electromechanical systems under the influence of attractive and repulsive Casimir forces between topological insulator plates as a function of their dielectric function and coating magnetization. The analysis of the Casimir force in the limit of strong and weak magnetization shows that the attractive force, which is produced for plate magnetizations in the same direction, is greater than the repulsive force that is produced for opposite magnetizations. However, both forces remain comparable for intermediate magnetizations. Moreover, for weak magnetization, the attractive force becomes stronger for an increasing dielectric function, while the opposite occurs for the repulsive force. On the other hand, increasing magnetization decreases the influence of the dielectric function on both the repulsive and attractive forces. Furthermore, for conservative systems, bifurcation and phase portrait analysis revealed that increasing magnetization decreases the regime of stable operation for devices with attractive forces, while their operation remains always stable under the presence of repulsive forces. Finally, for non-conservative periodically driven systems, the Melnikov function and Poincaré portrait analysis show that for magnetizations in the same direction leading to strong attractive Casimir forces, chaotic motion toward stiction is highly likely to occur preventing the long-term prediction of actuating dynamics. A remedy for this situation is obtained by the application of any magnetization in opposite directions between the interacting surfaces since the repulsive force makes it possible to prevent stiction.

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Chern-Simons boundary layers in the Casimir effect

Cited by 6 publications

References 49 publications

Perspective on Some Recent and Future Developments in Casimir Interactions

Perspective on Some Recent and Future Developments in Casimir Interactions

Casimir Interaction of Chern–Simons Layers on Substrates via Vacuum Stress Tensor

Nonlinear actuation of micromechanical Casimir oscillators with topological insulator materials toward chaotic motion: Sensitivity on magnetization and dielectric properties

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