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- W1519287856 abstract "AbstractThe Klein-Fock-Gordon equation is studied on the generalized Y-junction of Nstrings with a massive center. The corresponding formulas for wave scattering andnormal modes are obtained.Key words differential equations on networks, transmission rules, Klein-Fock-Gordon equation. 1 Introduction. Dynamical systems on manifolds are standard objects studied both in classical and quan-tum mechanics. Here we continue to study mechanics not on manifolds. The simplestexample of such a system gives a 3-ray star studied in [1] (see also [2] and [3]). This spaceis not a manifold. The problem became of special importance a couple decades ago afterthe discovery of D-branes. Problems of this type arise in different branches of Physics.String theory. Effectively strings are ordered sets of interacting harmonic oscillators andend of a string can belong to another string (D1-brane). Problem: describe the evolutionof excitations of the system.Nanoelectronics and theory of polymers. Nanoelectronics and theory of polymers are im-portant for modern technologies.The importance of this problem for strings is self evident. Gradually it becomes clearthat at the Planck scale matter manifests itself in form of strings, and a 3D-network ofsuperstrings can model the physical space [4], clearly leading to unification of all interac-tions, including gravitation.There are two types of problems (both in classical and quantum mechanics): (i) deter-mination of normal coordinates, (ii) description of scattering (i.e. description of evolution1" @default.
- W1519287856 created "2016-06-24" @default.
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- W1519287856 date "2009-08-08" @default.
- W1519287856 modified "2023-09-26" @default.
- W1519287856 title "A model with generalized Y-junction" @default.
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