Berry's Phase in Noncommutative Spaces

Alavi, S. A.

doi:10.1088/0256-307x/20/5/304

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…b the operator of total particle number at site i and ψ 0 N the ground-state wave function of a system with N particles. The Berry phase of the ground-state of the interacting system can be calculated using the twisted boundary condition which is defined as [43][44][45][46][47]…”

Section: Model and Methodsmentioning

confidence: 99%

Topological properties of one-dimensional hardcore Bose—Fermi mixture

et al. 2013

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We study the topological properties of a one-dimensional (1D) hardcore Bose—Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose—Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.

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Section: Model and Methodsmentioning

confidence: 99%

Topological properties of one-dimensional hardcore Bose—Fermi mixture

et al. 2013

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“…In this section we discuss the ''perturbation aspects of noncommutative dynamics''. The perturbation aspects of q-deformed dynamics in one dimensional q-spaces have been studied in [22] and [23]. Using…”

Section: Perturbation Aspects Of Noncommutative Dynamicsmentioning

confidence: 99%

Berry’s Phase in Noncommutative Spaces

Alavi

2003

Phys. Scr.

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“…Recently there have been much interest in the study of physics in noncommutative spaces(NCS) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], not only because the NCS is necessary when one studies the low energy effective theory of D-brane with B field background, but also because in the very tiny string scale or at very high energy situation, the effects of noncommutativity of space may appear. In the literatures the noncommutative quantum mechanics and noncommutative quantum field theory have been studied extensively and the main approach is based on the Weyl-Moyal correspondence which amounts to replacing the usual product by star product in a noncommutative space.…”

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confidence: 99%

General Noncommuting Curvilinear Coordinates and Fluid Mechanics

Alavi¹

2006

Chinese Phys. Lett.

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We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The cartesian , circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U (1) gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg-Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange to Euler map in fluid mechanics.

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Berry's Phase in Noncommutative Spaces

Cited by 3 publications

References 19 publications

Topological properties of one-dimensional hardcore Bose—Fermi mixture

Topological properties of one-dimensional hardcore Bose—Fermi mixture

Berry’s Phase in Noncommutative Spaces

General Noncommuting Curvilinear Coordinates and Fluid Mechanics

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