The Stark effect with minimum length

Louzada, H. L. C.; Belich, H.

doi:10.1142/s0217751x17500105

Cited by 4 publications

(5 citation statements)

References 25 publications

(29 reference statements)

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“…NCG in the presence of a deformed Heisenberg algebra has been considered for corrections in the hydrogen energy spectrum and Stark effect . The effects of NCG appearing in low energy scenarios are consequences of the generalized terms that do not appear in SM .…”

Section: Introductionmentioning

confidence: 99%

“…[8,9] In particular, it appears naturally in string theories [10,11] leading to effective theories describing SME that recover at low energy limits known physical results from SM.NCG in the presence of a deformed Heisenberg algebra has been considered for corrections in the hydrogen energy spectrum [12][13][14][15][16] and Stark effect. [17] The effects of NCG appearing in low energy scenarios are consequences of the generalized terms that do not appear in SM. [18][19][20][21][22] As such, it implies contributions in modified electromagnetism resulting in exotic electromagnetic properties.Here we investigate the exotic optical properties in the material response as a consequence of the modified electromagnetism by NCG.…”

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confidence: 99%

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Exotic Metamaterials from Noncommutative Theory

Prudencio

Belich

2018

Advcd Theory and Sims

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Exotic optical properties in materials are investigated as a consequence of noncommutative geometry (NCG) originated from deformed Heisenberg algebra. The NCG leads to modified eletromagnetism and then changes the constitutive relations that allow the determination of refractive index and impedance of the medium for different materials. Considering different situations where permittivity and permeability are obtained depending on NCG parameters, in dielectric, nonmagnetic, and magnetic cases, exotic conditions associated with metamaterial properties are obtained as the presence of negative index refraction under a generalized susceptibility depending on NCG. These results show that a class of optical metamaterials can be modeled based on NCG depending on noncommutative parameters.realized later that the noncommutative geometry (NCG) could be a scheme to extend the SM in several forms. [8,9] In particular, it appears naturally in string theories [10,11] leading to effective theories describing SME that recover at low energy limits known physical results from SM.NCG in the presence of a deformed Heisenberg algebra has been considered for corrections in the hydrogen energy spectrum [12][13][14][15][16] and Stark effect. [17] The effects of NCG appearing in low energy scenarios are consequences of the generalized terms that do not appear in SM. [18][19][20][21][22] As such, it implies contributions in modified electromagnetism resulting in exotic electromagnetic properties.Here we investigate the exotic optical properties in the material response as a consequence of the modified electromagnetism by NCG. We consider the case of material properties in particular and we take into account permittivity and permeability leading to metamaterial properties as negative index refraction, as a consequence of the dependence on a noncommutative parameter.The structure of this article is as follows: In Section 2, we revise NCG of the modified Heisenberg algebra; in Section 3, we discuss NCG and modified Maxwell equations; in Section 4, we discuss metamaterials from NCG-modified Maxwell equations; and in Section 5, we make our concluding remarks.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Exotic Metamaterials from Noncommutative Theory

Prudencio

Belich

2018

Advcd Theory and Sims

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“…The hydrogen atom is one of the simplest quantum systems that allows theoretical predictions of high accuracy, and is well-studied experimentally offering the most precise amount of measures [44]. There are many papers where the energy spectrum of the hydrogen atom in the presence minimum length is calculated [45,48,49], some of which have divergences in levels s (n = 1) [45], and recently it was studied the Stark effect with minimum length [46].…”

Section: Introductionmentioning

confidence: 99%

Metamaterials from modified CPT-odd standard model extension and minimum length

Prudencio,

Belich,

Louzada

2017

Preprint

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Here we discuss the standard model extension in the presence of CPT-odd Lorentz violation (LV) sector and of a deformed Heisenberg algebra that leads to a noncommutative theory with minimum length (ML). We derive the set of Maxwell equations emerging from this theory and considered the consequences with respect to the usual effects of electromagnetic waves and material media. We then considered the set of modified equations in material media and investigate the metamaterial behaviour as a consequence of LV and ML. We show that a negative index refraction can be derived from the presence of a non-commutativity suitably tuned by the β parameter, while in the presence of LV, we obtained the set of modified Maxwell equation in terms of the corresponding material fields with terms depending explicitly from the terms of interaction between the material fields depending on non-commutativity with the background field due to CPT-odd LV. We conclude that a new set of metamaterials can be derived as a consequence of CPT-odd LV and non-commutativity with minimum length.

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“…3)e 2 /m 0 c 2 , the term (e/c)l 0 u γ ∂ γ F iβ (x)u β could be actually interpreted as a leading (radiation) reaction force on m 0 since it is a small correction to the Newton-Lorentz force due to the applied field [21]. Finally, in (10), we have not considered other radiative reaction terms valid when the speed of the particle approaches the speed of light. These terms are nonlinear in the field tensor in the Landau-Lifshitz equation (LLE) [21].…”

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confidence: 99%

“…Many efforts have been made to build classical and quantum theories (a) E-mail: stanleybruces@gmail.com (b) E-mail: jdiaz@udec.cl founded on this view, such as the ones given in refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The essential conjecture in some of these theories is that on a quite short time δt the system does not evolve steadily under unitary evolution but somewhat in a succession of similar transformations.…”

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confidence: 99%