46 citations · 126 across the 26 of their papers we have counts for
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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…
Two-microlocal regularity of quasimodes on the torus
Fabricio Macià, Gabriel Rivière
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrödinger equation on two-dimensional flat tori. This is achieved by perfor…
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…
Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces
Nguyen Viet Dang, Gabriel Riviere
We prove the existence of a discrete correlation spectrum for Morse-Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with a…
Observability and quantum limits for the Schrödinger equation on the sphere
Fabricio Macià, Gabriel Riviere
In this note, we describe our recent results on semiclassical measures for the Schr{ö}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{…