35 citations · 85 across the 6 of their papers we have counts for
10 papers
Elementary cellular automata: spectral properties of Koopman operator for finite periodic realizations
Qingying Zhu, Serge Richard
In this paper we study Koopman operators associated with finite periodic realizations of elementary cellular automata. The spectra of these operators encompass various properties o…
Dirac operators on periodic planar graphs: the right definition advocated by flat bands
Koichi Kato, Daniel Parra, Serge Richard
Massive discrete Dirac-type operators on periodic planar graphs are investigated. Using Floquet--Bloch decomposition, we first show that neglecting the faces leads to spurious flat…
On some integral operators appearing in scattering theory, and their resolutions
S. Richard, T. Umeda
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of s…
Topological Levinson's theorem for inverse square potentials: complex, infinite, but not exceptional
H. Inoue, S. Richard
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators posse…
Quantum walks with an anisotropic coin II: scattering theory
S. Richard, A. Suzuki, R. Tiedra de Aldecoa
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum…
Quantum walks with an anisotropic coin I: spectral theory
S. Richard, A. Suzuki, R. Tiedra de Aldecoa
We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological ph…
Does Levinson's theorem count complex eigenvalues ?
F. Nicoleau, D. Parra, S. Richard
Yes it does ! Indeed an extended version of Levinson's theorem is proposed for a system involving complex eigenvalues. The perturbed system corresponds to a realization of the Schr…
Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition
S. Richard, R. Tiedra de Aldecoa
For the scattering system given by the Laplacian in a half-space with a periodic boundary condition, we derive resolvent expansions at embedded thresholds, we prove the continuity…
Low energy spectral and scattering theory for relativistic Schroedinger operators
S. Richard, T. Umeda
Spectral and scattering theory at low energy for the relativistic Schroedinger operator are investigated. Some striking properties at thresholds of this operator are exhibited, as…
Commutator methods for unitary operators
C. Fernandez, S. Richard, R. Tiedra de Aldecoa
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the…