Related papers: Fermions and Zeta Function on the Graph
We present first results of a mixed action project. We analyze gauge configurations generated with two flavors of dynamical twisted mass fermions. Neuberger's overlap Dirac operator is used for the valence sector. The various choices in the…
It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results…
Dynamical zeta functions are expected to relate the Schr\"odinger operator's spectrum to the periodic orbits of the corresponding fully chaotic Hamiltonian system. The relationsship is exact in the case of surfaces of constant negative…
We study the probability that a cycle of length k in the lattice [1, n]^s does not contain more lattice points than the k vertices of the cycle. Then we generalize this problem to other configurations induced by a given graph H,…
We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
The Fermi-Dirac and Bose-Einstein particles satisfy corresponding statistical distributions. In the phenomena of charge fractionalization and the fractional quantum Hall effect it is found that particles behave as if they are neither…
We study the coupling constant renormalization of gauge theories with an infinite multiplet of fermions, using the zeta function method to make sense of the infinite sums over fermions. If the gauge group K is the maximal compact subgroup…
A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we…
We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac…
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…
This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…
The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment…
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
Let $F$ be a number field and $D$ a quaternion algebra over $F$. Take a cuspidal automorphic representation $\pi$ of $D_\mathbb{A}^\times$ with trivial central cahracter. We study the zeta functions with period integrals on $\pi$ for the…
We consider the $N\!=\!1$ supersymmetric $\sigma$-model and we examine the transformation properties of the partition function under target-space duality. Contrary to what one would expect, we find that it is not, in general, invariant. In…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…