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Article
Correction to: Inverse spectral theory for semiclassical Jaynes–Cummings systems
We explain why Theorem B in the original article does not follow from the main result of this paper (Theorem A). While we conjecture that Theorem B should nevertheless be true, in this erratum we prove a sligh...
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Article
Symplectic Geometry and Spectral Properties of Classical and Quantum Coupled Angular Momenta
We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non-trivial way. These systems depend on a parameter
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Book
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Chapter
Schwartz Kernels
In this section we give a quick review of the notion of section distributions and Schwartz kernels of operators acting on spaces of sections of vector bundles. A good reference for this material is the classic...
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Chapter
Introduction
Berezin–Toeplitz operators appear in the study of the semiclassical limit of the quantisation of compact symplectic manifolds. They were introduced by Berezin [5], their microlocal analysis was initiated by Bo...
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Chapter
Berezin–Toeplitz Operators
As before, let \((M, \omega )\) ( M , ω ) be a prequantizable, compact, connected , let \(L \rightarrow M\) L → M be a prequantum line , and let \(\mathcal {H}_k\) H k be the as...
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Chapter
A Short Introduction to Kähler Manifolds
In this chapter, we recall some general facts about complex and Kähler manifolds. It is not an exhaustive list of such facts, but rather an introduction of objects and properties that we will need in the rest ...
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Chapter
Geometric Quantisation of Compact Kähler Manifolds
Let \((M, \omega )\) ( M , ω ) be a compact, connected, . The aim of this chapter is to construct a Hilbert space (or rather a family of Hilbert spaces) which will serve as the state space of quantum ...
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Chapter
Proof of Product and Commutator Estimates
The aim of this chapter is to prove Theorems 5.2.2 and 5.2.3.
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Chapter
Complex Line Bundles with Connections
Let us now recall some facts about complex line bundles. A certain number of definitions and properties could be stated for general vector bundles, but we prefer to focus on the one-dimensional case, since thi...
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Chapter
Asymptotics of the Projector \(\varPi _k\)
The goal of this chapter is to describe the asymptotic properties of the Schwartz kernel of the Szegő projector $$\varPi _k:L^2(M, L^k) \right...
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Chapter
Coherent States and Norm Correspondence
Finally, we prove the lower bound for the operator norm of a Berezin–Toeplitz . In order to do so, we use the so-called coherent states.
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Article
Inverse spectral theory for semiclassical Jaynes–Cummings systems
Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past decade. They include systems of high interest to phy...
