7 citations · 9 across the 5 of their papers we have counts for
6 papers · 1 filter
Spectrum of a non-selfadjoint quantum star graph
Gabriel Riviere, Julien Royer
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Ro…
Semiclassical behaviour of quantum eigenstates
Gabriel Rivière
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We…
Semiclassical asymptotics for nonselfadjoint harmonic oscillators
Victor Arnaiz, Gabriel Rivière
We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds o…
The quantum Loschmidt echo on flat tori
Gabriel Rivière, Henrik Ueberschaer
The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit…
Spectral analysis of morse-smale flows ii: resonances and resonant states
Nguyen Viet Dang, Gabriel Riviere
The goal of the present work is to compute explicitely the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents of the Morse--Smale flow, the topology of t…
Topology of Pollicott-Ruelle resonant states
Nguyen Viet Dang, Gabriel Riviere
We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associat…