REVIEW 3 cited by
Observability of the Schr{\"o}dinger equation with subquadratic confining potential in the Euclidean space
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We consider the Schr{\"o}dinger equation in $\mathbf{R}^d$, $d \ge 1$, with a confining potential growing at most quadratically. Our main theorem characterizes open sets from which observability holds, provided they are sufficiently regular in a certain sense. The observability condition involves the Hamiltonian flow associated with the Schr{\"o}dinger operator under consideration. It is obtained using semiclassical analysis techniques. It allows to provide with an accurate estimation of the optimal observation time. We illustrate this result with several examples. In the case of two-dimensional harmonic potentials, focusing on conical or rotation-invariant observation sets, we express our observability condition in terms of arithmetical properties of the characteristic frequencies of the oscillator.
Forward citations
Cited by 3 Pith papers
-
Quantitative observability for the Schr\"{o}dinger equation with an anharmonic oscillator
For the Schrödinger equation with potential |x|, the authors establish that sets whose complements are α-thin with α > 1/2 are observable at any time, while half-lines are never observable.
-
Egorov's theorem in the Weyl--H\"ormander calculus
A general Egorov theorem with quantified Ehrenfest time and full symbol expansion is proved via a new propagation result for quantum partitions of unity.
-
Smoothing effect and quantum-classical correspondence for the Schr{\"o}dinger equation with confining potential
For sub-quadratic confining potentials, the quantum smoothing effect and the classical escape rate of Hamiltonian trajectories are equivalent up to an O(1/R) factor.
Discussion (0). Continue with ORCID to comment.