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

For the standard torus $𝕋^{2} = ℝ^{2} ∕ ℤ^{2}$ , we prove observability for the free Schrödinger equation from a ball of radius $𝜖$ with explicit dependence on the observability constant on $𝜖$ .

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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

Vol. 3, No. 2, 2021

Zhongkai Tao

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors