Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces

2014/05/13 by Suresh Eswarathasan, Eswarathasan, Suresh, Gabriel Rivière +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1405.3231

openalex publication_date 2014/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small perturbations of the Schrödinger equation, and we prove that, in the semiclassical limit and for typical perturbations, the solutions become equidistributed on the unit cotangent bundle.

Citations

• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• The semiclassical zeta function for geodesic flows on negatively curved manifolds
• Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

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