9 citations · 54 across the 26 of their papers we have counts for
27 papers
Alternating Walk/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
We consider the alternating zeta function and the alternating -function of a graph , and express them by using the Ihara zeta function of . Next, we define a generalized a…
Ronkin/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato +1
The Ronkin function was defined by Ronkin in the consideration of the zeros of almost periodic function. Recently, this function has been used in various research fields in mathema…
Metzler/Zeta Correspondence
Yusuke Ide, Takashi Komatsu, Norio Konno +1
We present an explicit formula for the determinant on the Metzler matrix of a digraph . Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix o…
Mahler/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato +1
The Mahler measure was introduced by Mahler in the study of number theory. It is known that the Mahler measure appears in different areas of mathematics and physics. On the other h…
A Generalized Grover/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato +1
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 Grove…
CTM/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
In our previous work, we investigated the relation between zeta functions and discrete-time models including random and quantum walks. In this paper, we introduce a zeta function f…
A discontinuity of the energy of quantum walk in impurities
Kenta Higuchi, Takashi Komatsu, Norio Konno +2
We consider the discrete-time quantum walk whose local dynamics is denoted by at the perturbed region and free at the other positions. We obtain the station…
The trace formula with respect to the twisted Grover matrix of a mixed digraph
Takashi Komatsu, Sho Kubota, Norio Konno +1
We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As…
The scattering matrix with respect to an Hermitian matrix of a graph
Takashi Komatsu, Norio Konno, Iwao Sato
Recently, Gnutzmann and Smilansky presented a formula for the bond scattering matrix of a graph with respect to a Hermitian matrix. We present another proof for this Gnutzmann and…
IPS/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
Our previous works presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models including random walks, correlated random walks, quantum walks…
Walk/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
Our previous work presented explicit formulas for the generalized zeta function and the generalized Ihara zeta function corresponding to the Grover walk and the positive-support ve…
Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks
Takashi Komatsu, Norio Konno, Hisashi Morioka +1
We construct a distorted Fourier transformation associated with the multi-dimensional quantum walk. In order to avoid the complication of notations, almost all of our arguments are…
Grover/Zeta Correspondence based on the Konno-Sato theorem
Takashi Komatsu, Norio Konno, Iwao Sato
Recently the Ihara zeta function for the finite graph was extended to infinite one by Clair and Chinta et al. In this paper, we obtain the same expressions by a different approach…
A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph
Takashi Komatsu, Norio Konno, Iwao Sato
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph , and present a formula for the characteristic…
A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
Takashi Komatsu, Norio Konno, Iwao Sato
Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other…
Generalized eigenfunctions for quantum walks via path counting approach
Takashi Komatsu, Norio Konno, Hisashi Morioka +1
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-depen…
The limit theorem with respect to the matrices on non-backtracking paths of a graph
Takehiro Hasegawa, Takashi Komatsu, Norio Konno +4
We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the th moments of the arcsine law…
Explicit expression of scattering operator of some quantum walks on impurities
Takashi Komatsu, Norio Konno, Hisashi Morioka +1
In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of…
Zeta functions with respect to general coined quantum walk of periodic graphs
Takashi Komatsu, Norio Konno, Iwao Sato
We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite…
Eigenvalues of two-state quantum walks induced by the Hadamard walk
Shimpei Endo, Takako Endo, Takashi Komatsu +1
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed the distributions of the eigenvalues given by the splitt…
Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk
Takashi Komatsu, Norio Konno
In this paper, we consider the stationary measure of the Hadamard walk on the one-dimensional integer lattice. Here all the stationary measures given by solving the eigenvalue prob…
Stationary measure for three-state quantum walk
Takako Endo, Takashi Komatsu, Norio Konno +1
We focus on the three-state quantum walk(QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly,…
The Fourier and Grover walks on the two-dimensional lattice and torus
Masahiro Asano, Takashi Komatsu, Norio Konno +1
In this paper, we consider discrete-time quantum walks with moving shift (MS) and flip-flop shift (FF) on two-dimensional lattice and torus .…
Stationary measure for two-state space-inhomogeneous quantum walk in one dimension
Hikari Kawai, Takashi Komatsu, Norio Konno
We consider the two-state space-inhomogeneous coined quantum walk (QW) in one dimension. For a general setting, we obtain the stationary measure of the QW by solving the eigenvalue…