Quantum Hall effect on odd spheres

Coskun, U. H.
Kürkcüoğlu, Seçkin
Toga, G. C.
We solve the Landau problem for charged particles on odd dimensional spheres S2k-1 in the background of constant SO(2k - 1) gauge fields carrying the irreducible representation (I/2,I/2, . . . , I/2). We determine the spectrum of the Hamiltonian, the degeneracy of the Landau levels and give the eigenstates in terms of the Wigner D-functions, and for odd values of I, the explicit local form of the wave functions in the lowest Landau level (LLL). The spectrum of the Dirac operator on S2k-1 in the same gauge field background together with its degeneracies is also determined, and in particular, its number of zero modes is found. We show how the essential differential geometric structure of the Landau problem on the equatorial S2k-2 is captured by constructing the relevant projective modules. For the Landau problem on S-5, we demonstrate an exact correspondence between the union of Hilbert spaces of LLLs, with I ranging from 0 to I-max = 2K or I-max = 2K or I-max = 2K + 1 to the Hilbert spaces of the fuzzy CP3 or that of winding number +/- 1 line bundles over CP3 at level K, respectively.


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Global monochromatic solutions of the scalar wave equation axe obtained in flat wormholes of dimensions (2+1) and (3+1). The solutions are in the form of infinite series involving cylindrical and spherical wave functions, and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results presented in this work constitute instances of solutions of the scalar wave equation in a space-time admitting closed time-like curves.
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Quantum Hall effects on the complex Grassmann manifolds Gr(2)(C-N) are formulated. We set up the Landau problem in Gr(2()C(N)) and solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the SU(N) Wigner D functions for charged particles on Gr(2()C(N)) under the influence of Abelian and non-Abelian background magnetic monopoles or a combination of these. In particular, for the simplest case of Gr(2()C(4)), we explicitly write down the U(1) background gauge...
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
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The Dirac equation is solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number kappa under pseudospin and spin symmetry. The energy eigenvalues and the Dirac spinors are obtained in terms of hypergeometric functions. The energy eigenvalues are calculated numerically.
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Citation Formats
U. H. Coskun, S. Kürkcüoğlu, and G. C. Toga, “Quantum Hall effect on odd spheres,” PHYSICAL REVIEW D, pp. 0–0, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46860.