相关论文: Three-point correlations for quantum star graphs

In this thesis, we study Laplacian eigenfunctions on metric graphs, also known as quantum graphs. We restrict the discussion to standard quantum graphs. These are finite connected metric graphs with functions that satisfy Neumann vertex…

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…

A chain of quantum subgroups of the quantum automorphism group of finite graphs has been introduced. It generalizes the construction of J. Bichon (see [3]) in a sense. A better bound of the non zero eigenvalues of the graph Laplacian has…

The isoperimetric problem of maximizing all eigenvalues of the Laplacian on a metric tree graph within the class of trees of a given average edge length is studied. It turns out that, up to rescaling, the unique maximizer of the $k$-th…

We consider the density matrices derived from combinatorial laplacian matrix of graphs. Specifically, the star-relevant graph, which means adding certain edges on peripheral vertices of star graph, is the focus of this paper. Initially, we…

We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Robin Laplacian is close to the usual spectrum corresponding…

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…

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…

We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…

Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance…

This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…

With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo…

We extend the surgical tool box for quantum graphs to anti-standard and $\delta'$ vertex conditions. Monotonicity properties of eigenvalues of graph Laplacian with $\delta'$ interactions at vertices depend on the sign of vertex parameter.…

The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method…

We present a method to analytically compute the quantum corrected two-point correlation function of a scalar field in leading order at each loop in a homogeneous, isotropic and spatially flat spacetime where the expansion rate is time…

We study the first eigenvalue of the $p-$Laplacian (with $1<p<\infty$) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the…

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums…

We introduce the unbiased way statisticians look at the 2--point correlation function and study its relation to multifractal analysis. We apply this method to a simulation of the distribution of galaxy clusters in order to check the…

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of…

We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph…