Related papers: Multifractal eigenfunctions for quantum star graph…
In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT, together with a subsequent use of large, effective tight-binding Hamiltonians, allows to compute multifractal wave functions yielding the critical properties of…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We…
Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…
We discuss a basic thermodynamic properties of systems with multifractal structure. This is possible by extending the notion of Gibbs-Shannon's entropy into more general framework - Renyi's information entropy. We show a connection of…
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the…
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere aside from a sufficiently sparse set, then the…
The R\'enyi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the R\'enyi function is known explicitly. The theoretical part of…
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
This paper extends the theory of quantum fractional revival (QFR) on unitary Cayley graphs $X=(V(\mathbb{Z}_n),E(S))$ in several directions that remained unresolved in previous work. First, we investigate QFR with respect to the Laplacian…
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
We introduce a new method for constructing isospectral quantum graphs that is based on transplanting derivatives of eigenfunctions. We also present simple digraphs with the same reversing zeta function, which generalizes the Bartholdi zeta…
We show that if a graph $G$ has average degree $\bar d \geq 4$, then the Ihara zeta function of $G$ is edge-reconstructible. We prove some general spectral properties of the edge adjacency operator $T$: it is symmetric for an indefinite…