Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 22 for “"Topological invariants"”.
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Topological invariants of symplectic quotients
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Recognition of topological invariants by iterative arrays.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1969.
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Crystalline Topological Invariants in Invertible Fermionic States and Fractional Chern Insulators
Topological phases of matter have long been a central theme in condensed matter physics. When subject to certain symmetries, these phases are classified by topological invariants that often take fractional, quantized values. Despite significant theoretical advancements, major open questions remain …
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Fermions in Yang-Mills gauge theories: invariance, covariance and topology
… are particularly interested in the geometric and topological features in the problem. The complicated topological structures and properties present in these theories are made clear by elementary calculations in several simple models. We show explicitly how non-trivial phase and sign ambiguities …
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Disorder-driven phase transitions in weak, boundary-obstructed, and non-Hermitian topological insulators
… the effects of disorder on novel classes of topological insulators. Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of ""classical"" tenfold way …
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Topology and combinatorics of low genus mapping spaces to projective space
This thesis studies the topological invariants and boundary combinatorics of two classes of moduli spaces parametrising maps from elliptic curves to projective space - the Vakil--Zinger space and Kontsevich stable map spaces - combining the techniques of mixed Hodge structures, tropical moduli …
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Higher-order crystalline topology in resonator circuits
… is deformed. These fixed properties, known as topological invariants, are robust to any deformation of the material as long as it preserves both the energy gap and relevant symmetries. The discovery of materials hosting such invariants, known as topological insulators, was awarded the 2016 …
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Veering Triangulations: Theory and Experiment
… triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic …
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Mathematical models of soft elasticity: elastomers, active solids and topological metamaterials
… form of odd elasticity. In Part III, we consider topological mechanical metamaterials that exhibit robust floppy modes, characterised by topological invariants. To capture universal features of these modes in the continuum, we augment linear elasticity with additional fields and define a continuum …
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Rotational Symmetry and Phase Dynamics in Topological Superconductors
Topological superconductors are phases of matter that cannot be adiabatically connected to a trivial superconductor without closing the bulk gap or breaking some fundamental symmetry. Intimately tied to topological superconductors are Majorana bound states. These are neutral zero-energy …
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Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices
… models for noninteracting electronic topological phases of matter. The topological invariants associated with the boundary states are interpreted as winding numbers for windings around noncontractible loops on a Riemann sheet constructed using the algebraic structure of the transfer …
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Characterizing Zero Divisors of Group Rings
… is still open. The conjecture is about certain topological invariants attached to a group 𝐺. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group (the wreath product ℤ/2ℤ ≀ ℤ). We are interested in looking at …
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Topological Signatures for the Kitaev Chain in and out of Equilibrium
This thesis investigates aspects of the topological properties and non-equilibrium dynamics of one-dimensional quadratic fermionic systems, with a primary focus on the Kitaev chain and related lattice models. A unified theoretical framework is developed based on quadratic Hamiltonians, their …
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Qualitative representation and reasoning for spatial and spatio-temporal systems
… tables between different object types in the topological space. Further more, a study of the application of the methods in the spatio-temporal domain and in uncertain qualitative spaces is presented. The methodology used in this thesis guarantees completeness, in the sense that all …
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Topological Phases in Perovskite Iridates with Strong Spin-Orbit Coupling
The study of topological phases of matter has attracted much attention recently, providing a promising route to understanding the classification of various phases in condensed matter physics. The Iridates, which are Iridium-based compounds, have already shown rich physical phenomena and can be a …
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Aspects of symmetry, topology and anomalies in quantum matter
… quantum systems including symmetry-protected topological states (SPTs) and topologically ordered states (TOs). We first explore the ground state structures of SPTs and TOs: the former can be symmetry twisted and the latter has robust degeneracy. The Berry phases generated by transporting and …
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Mathematical and Computational Methods for the n-Body Problem
… intra- and trans-level distance metrics, and topological invariants such as the winding numbers. These diagnostics reveal the local and global organisation of the action landscape, distinguishing between minimum points, saddle-type solutions, and families of related orbits. The Thesis further …
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A study of knot-graphs
… or are given orientations which reflect certain topological properties of the knots concerned. First the properties of knot-graph adjacency matrices are studied. In particular, a matrix equation is derived which is shown to be satisfied by the α- and β-adjacency matrices of all knot-graphs; other …
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Topological Deep Learning: Graphs, Complexes, Sheaves
… topology. The "space'' in question is a topological space - a set with a neighbourhood structure - and the data attached to its neighbourhoods are algebraic objects like vector spaces. Since graphs, manifolds and everything in between is a topological space, we adopt this mathematical …
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Topological Insulating States in Photonics and Acoustics
<p>Recent surge of interest in topological insulators, insulating in their interior but conducting at the surfaces or interfaces of different domains, has led to the discovery of a variety of new topological states, and their topological invariants are characterized by numerous approaches in the …
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