Casimir Effect in Hemisphere Capped Tubes

Mello, E. R. Bezerra de; Saharian, A. A.

doi:10.1007/s10773-015-2758-0

Cited by 6 publications

(5 citation statements)

References 72 publications

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“…The results for Dirichlet and Neumann boundary conditions are obtained from those for the condition (2.2) in the limits β j → 0 and β j → ∞, A μ = 0, respectively. Robin type conditions appear in a variety of situations, including the considerations of vacuum effects for a confined charged scalar field in external fields [58], gauge field theories, quantum gravity and supergravity [56,57,59], braneworld models [60][61][62] and in a class of models with boundaries separating the spatial regions with different gravitational backgrounds [63][64][65]. In some geometries, these conditions may be useful for depicting the finite penetration of the field into the boundary with the "skindepth" parameter related to the coefficient β j .…”

Section: Andmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

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We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation. a

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Section: Andmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

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“…In carbon nanotubes, these contributions depend on the chirality of the tube and have been studied in [17]- [19]. The Casimir effect in a more complicated geometry of hemisphere capped tubes was considered in [20]. The condensed matter realizations of 2D fermions with curved geometries can be used to model the influence of the gravitational field on the quantum matter (for various types of mechanisms of the generation of curvature in graphene and the related effects see [21]).…”

Section: Introductionmentioning

confidence: 99%

The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons

et al. 2020

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We investigate the combined effects of boundaries and topology on the vacuum expectation values (VEVs) of the charge and current densities for a massive 2D fermionic field confined on a conical ring threaded by a magnetic flux. Different types of boundary conditions on the ring edges are considered for fields realizing two inequivalent irreducible representations of the Clifford algebra. The related bound states and zero energy fermionic modes are discussed. The edge contributions to the VEVs of the charge and azimuthal current densities are explicitly extracted and their behavior in various asymptotic limits is considered. On the ring edges the azimuthal current density is equal to the charge density or has an opposite sign. We show that the absolute values of the charge and current densities increase with increasing planar angle deficit. Depending on the boundary conditions, the VEVs are continuous or discontinuous at half-integer values of the ratio of the effective magnetic flux to the flux quantum. The discontinuity is related to the presence of the zero energy mode. By combining the results for the fields realizing the irreducible representations of the Clifford algebra, the charge and current densities are studied in parity and time-reversal symmetric fermionic models. If the boundary conditions and the phases in quasiperiodicity conditions for separate fields are the same the total charge density vanishes. Applications are given to graphitic cones with edges (conical ribbons).

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“…The edge-induced Casimir contributions in finite length carbon nanotubes were discussed in [48][49][50]. Tubes with more complicated curved geometries have been considered in [51][52][53][54]. These geometries provide exactly solvable examples to model the combined influence of gravity and topology on the properties of quantum matter.…”

Section: Introductionmentioning

confidence: 99%

Casimir Effect for Fermion Condensate in Conical Rings

2021

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The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones.

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Casimir Effect in Hemisphere Capped Tubes

Cited by 6 publications

References 72 publications

Casimir effect for scalar current densities in topologically nontrivial spaces

Casimir effect for scalar current densities in topologically nontrivial spaces

The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons

Casimir Effect for Fermion Condensate in Conical Rings

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