21 citations · 89 across the 16 of their papers we have counts for
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Stationary scattering theory for unitary operators with an application to quantum walks
Rafael Tiedra de Aldecoa
We present a general account on the stationary scattering theory for unitary operators in a two-Hilbert spaces setting. For unitary operators in Hilbert spaces ${\cal H}_0,…
Spectral and scattering theory of one-dimensional coupled photonic crystals
Giuseppe De Nittis, Massimo Moscolari, Serge Richard +1
We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals,…
Quantum time delay for unitary operators: general theory
Diomba Sambou, Rafael Tiedra de Aldecoa
We present a suitable framework for the definition of quantum time delay in terms of sojourn times for unitary operators in a two-Hilbert spaces setting. We prove that this time de…
Explicit formulas for the Schroedinger wave operators in R^2
S. Richard, R. Tiedra de Aldecoa
In this note, we derive explicit formulas for the Schroedinger wave operators in R^2 under the assumption that 0-energy is neither an eigenvalue nor a resonance. These formulas jus…
A few results on Mourre theory in a two-Hilbert spaces setting
S. Richard, R. Tiedra de Aldecoa
We introduce a natural framework for dealing with Mourre theory in an abstract two-Hilbert spaces setting. In particular a Mourre estimate for a pair of self-adjoint operators (H,A…
A formula relating localisation observables to the variation of energy in Hamiltonian dynamics
Antoine Gournay, Rafael Tiedra de Aldecoa
We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi…
On a new formula relating localisation operators to time operators
Serge Richard, Rafael Tiedra de Aldecoa
We consider in a Hilbert space a self-adjoint operator H and a family Phi=(Phi_1,...,Phi_d) of mutually commuting self-adjoint operators. Under some regularity properties of H with…
The method of the weakly conjugate operator: Extensions and applications to operators on graphs and groups
M. Mantoiu, S. Richard, R. Tiedra de Aldecoa
In this review we present some recent extensions of the method of the weakly conjugate operator. We illustrate these developments through examples of operators on graphs and groups…
Time delay for dispersive systems in quantum scattering theory. I. The Friedrichs model
Rafael Tiedra de Aldecoa
We present a method for proving the existence of time delay (defined in terms of sojourn times) as well as its identity with Eisenbud-Wigner time delay in the case of the Friedrich…
Anisotropic Lavine's formula and symmetrised time delay in scattering theory
Rafael Tiedra de Aldecoa
We consider, in quantum scattering theory, symmetrised time delay defined in terms of sojourn times in arbitrary spatial regions symmetric with respect to the origin. For potential…
Spectral analysis for convolution operators on locally compact groups
Marius Mantoiu, Rafael Tiedra de Aldecoa
We consider operators of convolution with measures on locally compact groups. We characterize the spectrum of by constructing auxiliary operators whose kernel conta…
On the spectrum of magnetic Dirac operators with Coulomb-type perturbations
Serge Richard, Rafael Tiedra de Aldecoa
We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assum…
Generalized definition of time delay in scattering theory
C. Gerard, R. Tiedra de Aldecoa
We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists…
Spectral analysis for adjacency operators on graphs
M. Mantoiu, S. Richard, R. Tiedra de Aldecoa
We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admis…
Time delay and short-range scattering in quantum waveguides
Rafael Tiedra de Aldecoa
Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue…
The nature of the essential spectrum in curved quantum waveguides
David Krejcirik, Rafael Tiedra de Aldecoa
We study the nature of the essential spectrum of the Dirichlet Laplacian in tubes about infinite curves embedded in Euclidean spaces. Under suitable assumptions about the decay of…