Quantum Hall Effect on Odd-Dimensional Spheres



Quantum Hall effect on odd spheres
Coskun, U. H.; Kürkcüoğlu, Seçkin; Toga, G. C. (2017-03-22)
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 f...
Quantum hall effect on grassmann manifolds
Ballı, Fatih; Kürkcüoğlu, Seçkin; Department of Physics (2014)
In this work we formulate Quantum Hall E ect(QHE) on Grassmann manifolds Gr2(CN). We, rst give a self-contained reviews of integer QHE on R2, S2 CP1 and CP2 which are oriented towards our purposes. Then, we set up the Landau problem on Gr2(CN) and discuss and formulate the wave functions, energy levels, degeneracy, incompressibility and spatial density properties. Group theoretical techniques are used to explore these properties for both abelian and non-abelian backgrounds and the wave functions are expr...
Quantum vacuum energy for massless conformal scalar field in Einstein and closed Friedmann universes
Özcan, Mustafa; Bayın, Selçuk Ş.; Department of Physics (1991)
Quantum mechanics on curved hypersurfaces
Olpak, Mehmet Ali; Tekin, Bayram; Department of Physics (2010)
In this work, Schrödinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac’s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the fir...
Quantum genetic algorithm method in self-consistent electronic structure calculations of a quantum dot with many electrons
Sahin, M; Atav, U; Tomak, Mehmet (World Scientific Pub Co Pte Lt, 2005-09-01)
In this study, we have calculated energy levels of an N-electron quantum dot. For this purpose, we have used two different techniques, matrix diagonalization and quantum genetic algorithm, to obtain simultaneous solutions of the coupled Schrodinger and Poisson equation in the Hartree approximation. We have determined single particle energy levels, total energy, chemical potential and capacitive energy. We have also compared the results, demonstrated the applicability of QGA to many-electron quantum systems ...
Citation Formats
S. Kürkcüoğlu, “Quantum Hall Effect on Odd-Dimensional Spheres,” 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/85575.