715 9 3628 1 10007 document 3628 2012_JoPhA_45_395305.pdf application/pdf ef87abc63ab822eb32eeaed1525f7bd1 MD5 398420 2014-01-30 15:32:10 http://eprints.iliauni.edu.ge/715/1/2012_JoPhA_45_395305.pdf 715 1 1 application/pdf text ge public

2012_JoPhA_45_395305.pdf

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http://eprints.org/relation/isVersionOf http://eprints.iliauni.edu.ge/id/document/3628 http://eprints.org/relation/isVolatileVersionOf http://eprints.iliauni.edu.ge/id/document/3628 http://eprints.org/relation/ispreviewThumbnailVersionOf http://eprints.iliauni.edu.ge/id/document/3628 3641 2 10032 document 3641 medium.jpg image/png 5fd1f4d79a3b171871f23df384ea6600 MD5 6029 2014-01-30 15:52:29 http://eprints.iliauni.edu.ge/715/4/medium.jpg 715 4 4 image/png other Thumbnails conversion from text to thumbnail_medium ge public

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http://eprints.org/relation/isVersionOf http://eprints.iliauni.edu.ge/id/document/3628 http://eprints.org/relation/isVolatileVersionOf http://eprints.iliauni.edu.ge/id/document/3628 http://eprints.org/relation/ismediumThumbnailVersionOf http://eprints.iliauni.edu.ge/id/document/3628 3642 2 10033 document 3642 small.jpg image/png 8dba83a8022bfee08a59b970c4b0dd95 MD5 1578 2014-01-30 15:52:30 http://eprints.iliauni.edu.ge/715/5/small.jpg 715 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/3628 http://eprints.org/relation/isVolatileVersionOf http://eprints.iliauni.edu.ge/id/document/3628 http://eprints.org/relation/issmallThumbnailVersionOf http://eprints.iliauni.edu.ge/id/document/3628 archive 34 disk0/00/00/07/15 2014-01-30 20:02:34 2015-04-03 06:20:08 2014-01-30 20:02:34 article show Eliashvili Merab Japaridze G.I. gia_japaridze@iliauni.edu.ge Tsitsishvili George pub QC fac_eng public The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of a homogeneous magnetic field. Provided the magnetic flux per uni t 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 the quantum group $U_q(sl_2)$ 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 allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying locations of the roots of polynomials on the complex plane are found. Employing numerical analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrammes exhibiting the ordered structure of one-particle eigenstates are depicted. 2012-09-12 published Journal of Physics A: Mathematical and General 45 9 Institute of Physics Publishing 395305-1 TRUE