LEADER 04802nam 22006735 450 001 9910303441503321 005 20200629121600.0 010 $a3-030-02212-9 024 7 $a10.1007/978-3-030-02212-9 035 $a(CKB)4100000007204991 035 $a(MiAaPQ)EBC5614218 035 $a(DE-He213)978-3-030-02212-9 035 $a(PPN)232964912 035 $a(EXLCZ)994100000007204991 100 $a20181211d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral Approach to Transport Problems in Two-Dimensional Disordered Lattices $ePhysical Interpretation and Applications /$fby Evdokiya Georgieva Kostadinova 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (116 pages) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 311 $a3-030-02211-0 327 $aChapter1. Introduction -- Chapter2. Theoretical Background -- Chapter3. Spectral Approach -- Chapter4. Delocalization in 2D Lattices of Various Geometries -- Chapter5. Transport in the Two-Dimentional Honeycomb Lattice with Substitutional Disorder -- Chapter6. Transport in 2D Complex Plasma Crystals -- Chapter7. Conclusions. 330 $aThis thesis introduces the spectral approach to transport problems in infinite disordered systems characterized by Anderson-type Hamiltonians. The spectral approach determines (with probability one) the existence of extended states for nonzero disorder in infinite lattices of any dimension and geometry. Here, the author focuses on the critical 2D case, where previous numerical and experimental results have shown disagreement with theory. Not being based on scaling theory, the proposed method avoids issues related to boundary conditions and provides an alternative approach to transport problems where interaction with various types of disorder is considered. Beginning with a general overview of Anderson-type transport problems and their relevance to physical systems, it goes on to discuss in more detail the most relevant theoretical, numerical, and experimental developments in this field of research. The mathematical formulation of the innovative spectral approach is introduced together with a physical interpretation and discussion of its applicability to physical systems, followed by a numerical study of delocalization in the 2D disordered honeycomb, triangular, and square lattices. Transport in the 2D honeycomb lattice with substitutional disorder is investigated employing a spectral analysis of the quantum percolation problem. Next, the applicability of the method is extended to the classical regime, with an examination of diffusion of lattice waves in 2D disordered complex plasma crystals, along with discussion of proposed future developments in the study of complex transport problems using spectral theory. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 606 $aCondensed matter 606 $aPhysics 606 $aPlasma (Ionized gases) 606 $aStatistical physics 606 $aMathematical physics 606 $aPartial differential equations 606 $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aPlasma Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P24040 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aCondensed matter. 615 0$aPhysics. 615 0$aPlasma (Ionized gases). 615 0$aStatistical physics. 615 0$aMathematical physics. 615 0$aPartial differential equations. 615 14$aCondensed Matter Physics. 615 24$aMathematical Methods in Physics. 615 24$aPlasma Physics. 615 24$aStatistical Physics and Dynamical Systems. 615 24$aMathematical Physics. 615 24$aPartial Differential Equations. 676 $a530.411 700 $aKostadinova$b Evdokiya Georgieva$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064830 906 $aBOOK 912 $a9910303441503321 996 $aSpectral Approach to Transport Problems in Two-Dimensional Disordered Lattices$92541130 997 $aUNINA