Related papers: Note on Green Function Formalism and Topological I…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
This paper is devoted to the study of the parameter's set where the Green's function related to a general linear $n^{\rm th}$-order operator, depending on a real parameter, $T_n[M]$, coupled with many different two point boundary value…
We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our…
This paper discusses the topological and transport properties of binary heterostructures of different topological materials. The creation of multilayer devices is an alternative to building synthetic topological materials. By adjusting the…
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…
Within the framework of many-particle perturbation theory, we develop an analytical approach that allows us to determine the small distance behavior of Green's functions and related quantities in electronic structure theory. As a case…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
The gauge invariant quark Green's function, defined with a path-ordered phase factor along a straight line, is studied in two-dimensional QCD in the large-N_c limit by means of an exact integrodifferential equation. It is found to be…
We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge…
In this paper we obtain an explicit formula of the parameter dependence of the partial derivatives of the Green's functions related to two-point boundary conditions. Such expression follows as an integral of both kernels times the…
In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter $\tau$). In this…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds,…
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…
A Green's function formalism is used to calculate the spectrum of localized modes of an impurity layer implanted within a ferromagnetic thin film. The equations of motion for the Green's functions are determined in the framework of the…
Let f be an entire function that has only finitely many critical and asymptotic values. Up to topological equivalence, the function $f$ is determined by combinatorial information, more precisely by an infinite graph known as a…
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…