Vol. 3, No. 2, 2021

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Exact control for the Schrödinger equation on the torus from small balls

Zhongkai Tao

Vol. 3 (2021), No. 2, 387–401
Abstract

For the standard torus 𝕋2 = 22, we prove observability for the free Schrödinger equation from a ball of radius 𝜖 with explicit dependence on the observability constant on 𝜖.

Keywords
quantum chaos, semiclassical analysis, control for Schrödinger equation, propagation of singularities
Mathematical Subject Classification
Primary: 35Q41, 35Q93, 47G30, 58J47
Milestones
Received: 4 August 2020
Revised: 10 March 2021
Accepted: 4 May 2021
Published: 31 July 2021
Authors
Zhongkai Tao
Department of Mathematics
University of California
Berkeley, CA
United States