Benjamin Alvarez: Spectral Analysis of a soft quantum waveguide coupled to a quantum scalar field

mardi 9 juin 2026, 10:30 → 11:30 Europe/Paris

Quantum waveguide and quantum field theory are two popular topics in mathematical physics. Both are important from a theoritcal point of view and have significant applications, such as optical fiber for quantum waveguides or positron emission tomography for quantum field theory. However, relatively few works investigate quantum field theory in waveguides. We believe that is an interesting direction to explore for a better undurstanding of physics and mathematics. For example, the study of two plates coupled with QED models leads to the so-called Casimir effect, widely discussed in the littérature

In this talk we consider a simple model in which a quantum particle is confined in a soft waveguide and interacts with a scalar field. The field does not interact with the waveguide. This system is modelled by a self-adjoint Hamiltonian for which we discuss the spectrum and derive binding conditions that guarentee the existance of a ground state

This is a joint work with Hugo Gouttenègre, with the support of Jean-Marie Barbaroux and Philippe Briet