相关论文: Spectrum of periodic chain graphs with time-revers…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral…
We discuss of a ring-shaped soft quantum wire modeled by $\delta$ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
The explicit solution to the spectral problem of quantum graphs found recently in \cite{Anima}, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to…
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…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Bipartite entanglement measures are fantastic tools to investigate quantum phases of correlated electrons. Here, I analyze the entanglement spectrum of **gapped** two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
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…
Quantum graphity is a background independent model for emergent geometry, in which space is represented as a complete graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however…