Related papers: Topological Resonances on Quantum Graphs
The probability representation of quantum and classical statistical mechanics is discussed. Symplectic tomography, center-of-mass tomography, and spin tomography are studied. The connection of tomographic probabilities with dynamic…
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical…
The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infinite number of vertices and provides various distortion…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
Single-photon super- and subradiance are important for the quantum memory and quantum information. We investigate one-dimensional atomic arrays under the spatially periodic magnetic field with a tunable phase, which provides a distinctive…
We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. We…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…
We introduce asymptotic-M\"obius (AM) maps, a large-scale analogue of quasi-M\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem…
We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
We demonstrate that a quantum graph exhibits a $\mathcal{PT}$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not…
Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal…