Related papers: Magnetic ring chains with vertex coupling of a pre…
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
We show that strong pairing correlations in Fermi gases lead to the appearance of a gap-like structure in the RF-spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average RF-shift…
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands,…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement…
We construct groundstates of the string with non-zero mass gap and non-trivial chromo-magnetic fields as well as curvature. The exact spectrum as function of the chromo-magnetic fields and curvature is derived. We examine the behavior of…
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…
Hofstadter's diagram, or the energy spectrum against the magnetic field in tight-binding systems, is obtained for the models having flat (dispersionless) one-electron band(s) that have originally been proposed for itinerant spin…
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace formulae is obtained which link together two…
In a ferromagnetic spin chain, the control of the local effective magnetic field allows to manipulate the static and dynamical properties of entanglement. In particular, the propagation of quantum correlations can be driven to a great…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second…
The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
The energy and persistent current spectra for a relativistic fermion on a ring is studied in details. The nonlinear nature of persistent current in relativistic regime and its dependence on particle mass and ring radius are analysed…
A first-principle study of the collective oscillation spectrum of a strongly correlated one-component plasma in a strong magnetic field is presented. The spectrum consists of six fundamental modes which are found to be in good agreement…
We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of an Erd\H{o}s-R\'enyi graph is cospectral when the average…
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 define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…