"Kvantov\u00E9 grafy a p\u0159\u00EDbuzn\u00E9 syst\u00E9my" . "IAA1048101" . "quantum graphs" . . "0"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=IAA1048101"^^ . "0"^^ . "In mesoscopic research and other parts of physics we often meet quantum mechanical systems whose configuration space is a graph, or such that interact with can be modeled by a graph. They offer on apportunity to study relations between spectral and transport properties of such systems and their geometrical and topological characteristics. The aim of the project is a thourough analysis of interesting classes of quantum graphs, both finite and infinite, including the bound state structure and different spectral types. We shall investigate also their classical counterparts, in the first place from the viewpoint of relations between the integrable and chaotic behaviour. We shall study also generalizd graphs whose elements may be manifolds of different dimensions. Furthermore, we shall formulate conditions under which graphs are appropriate models formore complicated systems composed of quantum wires and dots, photonic crystals, etc."@en . "Quantum graphs and related systems"@en . "quantum graphs; spectral and transport properties; generalized graphs; quantum waveguides"@en . . . . . "37"^^ . "P\u0159i studiu mesoskopick\u00FDch objekt\u016F i v jin\u00FDch oblastech fyziky se st\u00E1le \u010Dast\u011Bji setk\u00E1v\u00E1me s kvantov\u011Bmechanick\u00FDmi syst\u00E9my, jejich\u017E konfigura\u010Dn\u00ED prostor m\u00E1 podobu grafu, p\u0159\u00EDpadn\u011B takov\u00FDmi, kter\u00E9 interaguj\u00ED s vn\u011Bj\u0161\u00EDm polem, je\u017E lze pomoc\u00ED grafu modelovat. Ty nab\u00EDzej\u00ED v\u00FDhodnou p\u0159\u00EDle\u017Eitost pro studium vztah\u016F mezi spektr\u00E1ln\u00EDmi a transportn\u00EDmi vlastnostmi na jedn\u00E9 stran\u011B a geometrick\u00FDmi, resp. topologick\u00FDmi charakteristikami takov\u00FDch soustav na stran\u011B druh\u00E9. C\u00EDlem projektu je podrobn\u00E1 anal\u00FDza zaj\u00EDmav\u00FDch t\u0159\u00EDd kvantov\u00FDch graf\u016F, kone\u010Dn\u00FDch i nekone\u010Dn\u00FDch, v\u010Detn\u011B struktury v\u00E1zan\u00FDch stav\u016F a r\u016Fzn\u00FDch typ\u016F spekter. Budeme se zab\u00FDvat tak\u00E9 jejich klasick\u00FDmi prot\u011Bj\u0161ky, p\u0159edev\u0161\u00EDm z hlediska vztahu mezi \u0159e\u0161iteln\u00FDm a chaotick\u00FDm dynamick\u00FDm chov\u00E1n\u00EDm. Vy\u0161et\u0159\u00EDme i zobecn\u011Bn\u00E9 grafy, jejich\u017E prvky mohou b\u00FDt variety r\u016Fzn\u00FDch dimens\u00ED. D\u00E1le se v\u011Bnujeme formulaci podm\u00EDnek, za kter\u00FDch jsou grafy vhodn\u00FDm modelem pro slo\u017Eit\u011Bj\u0161\u00ED syst\u00E9my tvo\u0159en\u00E9 kvantov\u00FDmi dr\u00E1ty a te\u010Dkami, fotonov\u00FDmi krystaly apod." . . . "2004-10-13+02:00"^^ . "37"^^ . . . . . . . . " generalized graphs" . . " spectral and transport properties" . "byla odvozena \u0159ada nezn\u00E1m\u00FDch spektr\u00E1ln\u00EDch a transportn\u00EDch vlastnost\u00ED pro kvantov\u00E9 syst\u00E9my, jejich\u017E pohyb je omezen na graf nebo jeho okol\u00ED. V\u00FDsledky pom\u00E1haj\u00ED l\u00E9pe ch\u00E1pat vlastnosti r\u016Fzn\u00FDch nanostruktur z polovodi\u010Dov\u00FDch a jin\u00FDch materi\u00E1l\u016F."@cs . . "3"^^ .