841 9 3626 1 9991 document 3626 2012_Proc_RMI_160_35.pdf application/pdf a79ec9de938a77d2fb78185142413b51 MD5 328708 2014-01-30 14:36:14 http://eprints.iliauni.edu.ge/841/1/2012_Proc_RMI_160_35.pdf 841 1 1 application/pdf text ge public

2012_Proc_RMI_160_35.pdf

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http://eprints.org/relation/isVersionOf http://eprints.iliauni.edu.ge/id/document/3626 http://eprints.org/relation/isVolatileVersionOf http://eprints.iliauni.edu.ge/id/document/3626 http://eprints.org/relation/ismediumThumbnailVersionOf http://eprints.iliauni.edu.ge/id/document/3626 3637 2 10023 document 3637 small.jpg image/png 342e9082b965f4539cbafdbad39e9d81 MD5 1327 2014-01-30 15:46:47 http://eprints.iliauni.edu.ge/841/5/small.jpg 841 5 5 image/png other Thumbnails conversion from text to thumbnail_small ge public

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http://eprints.org/relation/isVersionOf http://eprints.iliauni.edu.ge/id/document/3626 http://eprints.org/relation/isVolatileVersionOf http://eprints.iliauni.edu.ge/id/document/3626 http://eprints.org/relation/issmallThumbnailVersionOf http://eprints.iliauni.edu.ge/id/document/3626 archive 34 disk0/00/00/08/41 2014-01-30 20:03:20 2015-04-03 06:20:28 2014-01-30 20:03:20 article show Eliashvili Merab Japaridze G.I. gia_japaridze@iliauni.edu.ge Tsitsishvili George pub QC fac_eng public The tight-binding model of electrons on a honeycomb lattice is studied in the presence of a homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux the one-particle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations on a complex plane. For the special values of quasi-momentum the entangled system admits solutions in terms of polynomials. In that case the system exhibits certain symmetry relations allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying the locations of the roots of polynomials on a complex plane and consequently the one-particle wave functions are found. Employing numeric analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of one-particle states are depicted. 2012-12 published Proceedings of A. Razmadze Mathematical Institute 160 3 A. Razmadze Mathematical Institute 35-51 TRUE