Induced fermionic charge and current densities in two-dimensional rings

Bellucci, Stefano; Saharian, A. A.; Grigoryan, A. K.

doi:10.1103/physrevd.94.105007

Cited by 10 publications

(11 citation statements)

References 95 publications

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“…Note that the fermionic condensate, the charge and current densities in (2+1)-dimensional conical spacetime with a single and two circular boundaries have been investigated in [57,60,61,62]. The geometry of a planar ring has been considered in [63].…”

Section: Asymptotics Of the Current Density And Numerical Resultsmentioning

confidence: 99%

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

Bellucci,

Santos,

de Mello

et al. 2020

Preprint

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We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z 2 -symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the branefree and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C-and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

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Section: Asymptotics Of the Current Density And Numerical Resultsmentioning

confidence: 99%

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

Bellucci,

Santos,

de Mello

et al. 2020

Preprint

Self Cite

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“…The fermionic current density induced by a magnetic flux in planar graphene rings with circular edges has been recently investigated in [41]. The fermionic field was confined in the circular ring by the bag boundary conditions on the edges.…”

Section: Parity and Time-reversal Symmetric Odd-dimensional Modelsmentioning

confidence: 99%

Fermionic currents in topologically nontrivial braneworlds

et al. 2018

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We investigate the influence of a brane on the vacuum expectation value (VEV) of the current density for a charged fermionic field in background of locally AdS spacetime with an arbitrary number of toroidally compact dimensions and in the presence of a constant gauge field. Along compact dimensions the field operator obeys quasiperiodicity conditions with arbitrary phases and on the brane it is constrained by the bag boundary condition. The brane is parallel to the AdS boundary and it divides the space into two regions with different properties for the fermionic vacuum. In both these regions, the VEVs for the charge density and the components of the current density along uncompact dimensions vanish. The components along compact dimensions are decomposed into the brane-free and brane-induced contributions. The behavior of the latter in various asymptotic regions of the parameters is investigated. It particular, it is shown that the brane-induced contribution is mainly located near the brane and vanishes on the AdS boundary and on the horizon. An important feature is the finiteness of the current density on the brane. Applications are given to Z 2 -symmetric braneworlds of the Randall-Sundrum type with compact dimensions for two classes of boundary conditions on the fermionic field. For the second one we show that the contribution of the brane to the current does not vanish when the location of the brane tends to the AdS boundary. In odd spacetime dimensions, the fermionic fields realizing two inequivalent irreducible representations of the Clifford algebra and having equal phases in the periodicity conditions give the same contribution to the vacuum current density. Combining the contributions from these fields, the current density in odd-dimensional C-,Pand T -symmetric models is obtained. In the special case of three-dimensional spacetime, the corresponding results are applied for the investigation of the edge effects on the ground state current density induced in curved graphene tubes by an enclosed magnetic flux.

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“…The effects of finite temperature on the FC were investigated in [77,78]. The vacuum expectation values for the charge and current densities on planar rings have been studied in [79].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for fermion condensate in conical rings

Saharian,

Petrosyan,

Hovhannisyan

2021

Preprint

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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-Planatype 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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Induced fermionic charge and current densities in two-dimensional rings

Cited by 10 publications

References 95 publications

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

Fermionic currents in topologically nontrivial braneworlds

Casimir effect for fermion condensate in conical rings

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