Re-gauging Groupoid, Symmetries and Degeneracies for Graph Hamiltonians and Applications to the Gyroid Wire Network
نویسندگان
چکیده
Motivated by Harper Hamiltonians on skeletal graphs and their C∗–geometry, we study a certain class of graph Hamiltonians. These Hamiltonians can be thought of as a finite groupoid representation in separable Hilbert spaces. Here the groupoid is the path groupoid of a finite graph. Given such a setup, we consider the possible matrix versions of the Hamiltonian, which are indexed by the choice of a rooted spanning tree and an order of the vertices. The first result is that all the matrix representations are linked to each other via the conjugation action of a re–gauging
منابع مشابه
Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid
Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of An type sin...
متن کاملSingular Geometry of the Momentum Space: from Wire Networks to Quivers and Monopoles
A new nano–material in the form of a double gyroid has motivated us to study (non)–commutative C∗ geometry of periodic wire networks and the associated graph Hamiltonians. Here we present a general more abstract framework, which is given by certain quiver representations, with special attention to the original case of the gyroid as well as related cases, such as graphene. The resulting effectiv...
متن کاملThe geometry of the double gyroid wire network: quantum and classical
Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a double gyroid wire network. We use methods of commutative and noncommutative geometry to describe this wire network. Its noncommutative geometry is closely related to noncommutative 3-tori as we discuss in detail. Mathematics Subject Classification (2010). 46L60, 81R60, 58B34, 53...
متن کاملExperimental investigation for wake of the circular cylinder by attaching different number of tripping wires
An experimental study is conducted on flow past a circular cylinder fitted with some tripping wires on its surface. The work investigates the dependency of the critical wire locations on the wire size and Reynolds numbers, and examines the wake and vortex shedding characteristics in an effort to advance the understanding of the critical wire effects beyond the existing literature. The primary a...
متن کاملA Novel Approach for Detecting Relationships in Social Networks Using Cellular Automata Based Graph Coloring
All the social networks can be modeled as a graph, where each roles as vertex and each relationroles as an edge. The graph can be show as G = [V;E], where V is the set of vertices and E is theset of edges. All social networks can be segmented to K groups, where there are members in eachgroup with same features. In each group each person knows other individuals and is in touch ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012