Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

Wang, Bingqian; Long, Zheng-Wen; Long, Chao-Yun; Wu, Shurui

doi:10.1088/1674-1056/27/1/010301

Cited by 20 publications

(11 citation statements)

References 45 publications

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“…[1] Many kinds of noncommutative spaces have been studied by physicists and mathematicians, such as the Moyal plane and fuzzy space. [2][3][4][5][6][7][8][9][10][11] The phase space in quantum mechanics is also a Moyal-type noncommutative space, because the position and momentum operators satisfy the noncommutative Heisenberg algebras.…”

Section: Introductionmentioning

confidence: 99%

Connes distance of 2D harmonic oscillators in quantum phase space*

Lin¹,

Heng²

2021

Chinese Phys. B

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We study the Connes distance of quantum states of two-dimensional (2D) harmonic oscillators in phase space. Using the Hilbert–Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert space, and obtain the Dirac operator and a spectral triple corresponding to a four-dimensional (4D) quantum phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements. We construct the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of 2D quantum harmonic oscillators. We prove that these two-dimensional distances satisfy the Pythagoras theorem. These results are significant for the study of geometric structures of noncommutative spaces, and it can also help us to study the physical properties of quantum systems in some kinds of noncommutative spaces.

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Section: Introductionmentioning

confidence: 99%

Connes distance of 2D harmonic oscillators in quantum phase space*

Lin¹,

Heng²

2021

Chinese Phys. B

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“…The deformed momentum operators will almost inevitably cause Hamiltonians of all quantum mechanical systems to be corrected. Since Kempf and his colleagues established the theoretical framework of quantum mechanics based on generalized uncertainty, the studies of Schrödinger equation, [13][14][15][16][17][18][19][20][21][22][23][24][25][26] the Dirac equation, [27][28][29][30][31][32][33][34][35][36][37][38] K-G equation [39][40][41] and DKP equation [42][43][44][45][46][47][48][49][50] get great interest, and some phenomena in black hole remnants, 51,52 the trans-Planckian problem of inflation, 53,54 and the cosmological constant problem 55,56 can be explained by generalized uncertainty relations. On the quantum level, except for the bound state, some related works on scattering state have been reported.…”

Section: Introductionmentioning

confidence: 99%

Scattering in graphene quantum dots under generalized uncertainty principle

Long

et al. 2019

Int. J. Mod. Phys. A

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In this article, the Dirac electron scattering problem on circular barrier of radius [Formula: see text] is studied under the generalized uncertainty principle (GUP). The expressions of scattering coefficients, scattering cross-section and scattering efficiency of massless Dirac particle are obtained by solving the massless Dirac equation under GUP and discussed by numerical methods. It shows that the scattering coefficient, the scattering cross-section, and the scattering efficiency depend explicitly on the GUP parameter [Formula: see text]. For the scattering coefficient [Formula: see text], GUP may cause slight shift in the oscillation position of [Formula: see text] and make some peaks value of [Formula: see text] smaller. For scattering cross-section and scattering efficiency, GUP may also lead to slight shift in their oscillation position and increase of amplitude when the GUP parameter increases.

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“…For instance, distortions of energy levels of atoms [15][16][17][18][19][20], contributions to the topological phase effects [11,12,[21][22][23][24][25][26], corrections on the spin-orbital interactions [27][28][29][30][31][32], as well as deformations of quantum speeds of relativistic charged particles [33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Chiral Spin Noncommutative Space and Anomalous Dipole Moments

2019

Preprint

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We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and the maps are represented by a spin-dependent translation operator. Based on the maps, gauge field theory in chiral spin noncommutative space is established. The corresponding gauge transformations are induced by a local phase rotation on commutative functions, and hence are consistent with the ordinary gauge transformations by definition. Furthermore, a general extension of the ordering between Dirac matrix and gauge potential is introduced. Noncommutative corrections on equations of motion of matter and gauge fields are studied. We find that there are two kinds of corrections. The first kind of correction involves derivatives of the matter field, and hence contribute the ordinary Noether current. On the other hand, the second kind of correction depends only on derivatives of the gauge fields, and hence contribute anomalous magnetic and electric dipole moments of the matter field. Moreover, experimental bounds on the noncommutative parameters for muon lepton are studied in a simplified model.

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Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

Cited by 20 publications

References 45 publications

Connes distance of 2D harmonic oscillators in quantum phase space*

Connes distance of 2D harmonic oscillators in quantum phase space*

Scattering in graphene quantum dots under generalized uncertainty principle

Chiral Spin Noncommutative Space and Anomalous Dipole Moments

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