Integrals containing products of Airy functions and planar photon propagation in a magnetic field

Schubert, Christian; Варламов, В.В.

doi:10.1002/mma.1471

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…• Our procedure is an alternative to the traditional approach, in which the vacuum polarization tensor is expressed as a double proper time integral [23,[26][27][28]. In fact, for the particular case of QED in (2 + 1) dimensions considered in [28], the weak field expansion of the polarization scalars, equations ( 48)-(50) of that reference, match our findings in the massless limit, when we set = v 1 F .…”

Section: A Continuous Model For Graphenesupporting

confidence: 65%

“…• Our procedure is an alternative to the traditional approach in which the vacuum polarization tensor is expressed as a double proper time integral [21,24,25,26]. In fact, for the particular case of QED in (2+1)-dimensions considered in Ref.…”

Section: A Continuous Model For Graphenementioning

confidence: 99%

“…QED 3 , being superrenormalizable, lacks UV-regularization issues. We have presented an alternative calculation to the standard representation of the polarization tensor as a double proper time integral [23,[26][27][28], which manifestly preserves gauge invariance.…”

Section: Final Remarksmentioning

confidence: 99%

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Graphene transparency in weak magnetic fields

Valenzuela¹,

Hernández-Ortíz²,

Loewe³

et al. 2015

J. Phys. A: Math. Theor.

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Abstract. We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity B perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order (eB) 2 , where e is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is radiated with monochromatic light of frequency ω along the external field direction, from the modified Maxwell's equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal (σxx) and transverse (σxy) conductivities. Corrections to these quantities, both calculated and measured, are of order (eB) 2 /ω 4 . Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.

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Section: A Continuous Model For Graphenesupporting

confidence: 65%

Section: A Continuous Model For Graphenementioning

confidence: 99%

See 1 more Smart Citation

Graphene transparency in weak magnetic fields

Valenzuela¹,

Hernández-Ortíz²,

Loewe³

et al. 2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…• Our procedure is an alternative to the traditional approach in which the vacuum polarization tensor is expressed as a double proper time integral [21,24,25,26].…”

Section: A Continuous Model For Graphenementioning

confidence: 99%

Graphene transparency in weak magnetic fields

Valenzuela,

Hernández-Ortiz,

Loewe

et al. 2014

Preprint

View full text Add to dashboard Cite

We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity B perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order (eB) 2 , where e is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is radiated with monochromatic light of frequency ω along the external field direction, from the modified Maxwell's equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal (σxx) and transverse (σxy) conductivities. Corrections to these quantities, both calculated and measured, are of order (eB) 2 /ω 4 . Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.

show abstract

“…As far as we know, it was the first case when the integral of Airy function power results in a logarithmic function value. Products of two Airy functions and their integral transforms are investigated in many mathematical and physical papers (see, for example, [3][4][5][6][7][8]) while products of three or more Airy functions meet quite rarely. Besides the Laurenzi paper [1], these products are discussed in [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%