相关论文: Spectral properties of hexagonal lattices with the…

Flux-energy and angle-energy diagrams for an exact three-dimensional Hamiltonian of the Bloch electron in a uniform magnetic field are analyzed. The dependence of the structure of the diagrams on the direction of the field, the geometry of…

Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…

The spectral and transport properties of a non-Hermitian tight-binding lattice with unidirectional hopping are theoretically investigated in three different geometrical settings. It is shown that, while for the infinitely-extended (open)…

This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex…

Let $\Gamma$ be an arbitrary $\mathbb{Z}^n$-periodic metric graph, which does not coincide with a line. We consider the Hamiltonian $\mathcal{H}_\varepsilon$ on $\Gamma$ with the action $-\varepsilon^{-1}{\mathrm{d}^2/\mathrm{d} x^2}$ on…

We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the…

For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.

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…

We characterize the graphs with loops whose degree sequences have no repeated values and find their adjacency spectrum. In the case of simple graphs, such graphs are called anti-regular graphs and are examples of threshold graphs. The…

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is…

In this paper, we introduce a graph structure called linear dependence graph of a finite dimensional vector space over a finite field. Some basic properties of the graph like connectedness, completeness, planarity, clique number, chromatic…

Twisted trilayer graphene hosts two moir\'e superlattices originating from two interfaces between graphene layers. However, the system is generally unstable to lattice relaxation at small twist angles and is expected to show a significantly…

Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…

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…

Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial…

In this paper we study the energy spectrum of a two dimensional electron gas (2DEG) in a two dimensional periodic magnetic field. Both a square magnetic lattice and a triangular one are considered. We consider the general case where the…

Earlier work showed that the track in the X-ray hardness-intensity diagram of Cir X-1 corresponds to a Z track in its color-color diagram. In this paper, we study the cross spectrum of Cir X-1 in different regions of the hardness-intensity…

We suggest and experimentally realize a spectral photonic lattice - a signal can hop between discrete frequency channels, driven by nonlinear interaction with stronger pump lasers. By controlling the complex envelope and frequency…

We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by $\pm 1$.…

It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are…