Berry’s Phase in Noncommutative Spaces

Alavi, S. A.

doi:10.1238/physica.regular.067a00366

Cited by 10 publications

(7 citation statements)

References 23 publications

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“…In quantum mechanics, a great number of problems have been investigated in the case of noncommutative space [29] and phase-space. Some important results obtained are related to geometric phases, such as the Aharonov-Bohm effect [30,31,32,33,34], the Aharonov-Casher effect [35,36], the Berry quantum phase [37,38], Landau levels [39,40,41] and others that involve dynamics of dipoles [42]. In a recent paper, we analyzed the quantum geometrical phase effect for a quantum neutral particle with permanent magnetic and electric dipole moments in the presence of external magnetic and electric fields, proposed by Anandan [43], in the noncommutative space and phase space quantum mechanics context [44].…”

Section: Introductionmentioning

confidence: 99%

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Landau analog levels for dipoles in non-commutative space and phase space

Ribeiro¹,

Passos²,

Furtado³

et al. 2008

Eur. Phys. J. C

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In the present contribution we investigate the Landau analog energy quantization for neutral particles, that possesses a nonzero permanent magnetic and electric dipole moments, in the presence of an homogeneous electric and magnetic external fields in the context of the noncommutative quantum mechanics. Also, we analyze the Landau-Aharonov-Casher and Landau-He-McKellar-Wilkens quantization due to noncommutative quantum dynamics of magnetic and electric dipoles in the presence of an external electric and magnetic fields and the energy spectrum and the eigenfunctions are obtained. Furthermore, we have analyzed Landau quantization analogs in the noncommutative phase space, and we obtain also the energy spectrum and the eigenfunctions in this context. * Electronic address: lrr,passos,jroberto,furtado@fisica.ufpb.br

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Landau analog levels for dipoles in non-commutative space and phase space

Ribeiro¹,

Passos²,

Furtado³

et al. 2008

Eur. Phys. J. C

View full text Add to dashboard Cite

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“…In recent years there have been a lot of work devoted to the study of noncommutative field theory or noncommutative quantum mechanics and possible experimental consequences of extensions of the standard formalism [2][3][4][5][6][7][8][9][10][11][12][13]. In the last few years there has been also a growing interest in probing the space-space noncommutativity effects on cosmological observations [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Running of the Spectral Index in Noncommutative Inflation

Alavi

Nasseri

2005

Int. J. Mod. Phys. A

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Abstract:We study the cosmological implications of the space-space noncommutative inflation and present formulae for the spectral index and its running. Our results show that deviations from the spectral index and its running depend on the space-space noncommutativity length scale. We conclude that in the slow-roll regime of a typical inflationary scenario, space-space noncommutativity has negligible effects on both the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. The results show that the correction terms to the commutative case are positive for the spectral index and negative for the running of the spectral index. Nevertheless the spectral index in noncommutative spaces is less than one owing to the very small values of the correction terms.

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“…[11][12][13][14][15][16][17][18][19] In the last few years there has been also a growing interest in probing the space-space noncommutativity effects on cosmological observations. 20- 25 We will use the natural units system that sets k B , c, and all equal to one, so that P = M −1 P = √ G. To read easily this article we also use the notation D t instead of D(t), which means that the space dimension D is a function of time.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative Decrumpling Inflation and Running of the Spectral Index

Nasseri

Alavi

2005

Int. J. Mod. Phys. D

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We present a new inflation model, known as noncommutative decrumpling inflation, in which space has noncommutative geometry with time variability of the number of spatial dimensions. Within the framework of noncommutative decrumpling inflation, we compute both the spectral index and its running. Our results show the effects of both time variability of the number of spatial dimensions and noncommutative geometry on the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. We conclude that the effects of noncommutative geometry on the spectral index and its running are much smaller than the effects of time variability of spatial dimensions.

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Berry’s Phase in Noncommutative Spaces

Cited by 10 publications

References 23 publications

Landau analog levels for dipoles in non-commutative space and phase space

Landau analog levels for dipoles in non-commutative space and phase space

Running of the Spectral Index in Noncommutative Inflation

Noncommutative Decrumpling Inflation and Running of the Spectral Index

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