Searching for my papers on other websites is not always obvious, because of the various (mis)spellings of my name (including accented characters). If you have access to MathSciNet, this is your best bet, they are good at this. Here are some links with incomplete data you may try: ArXiv, HAL.

Here are the correct spellings. Any other combination is wrong, but many can be found online unfortunately...

• San Vu Ngoc
• San Vũ Ngọc

#### Vietnamese ordering:

• Vu Ngoc San
• Vũ Ngọc San

The list below is produced from my BibTeX file. Here is also a more traditional PDF version.

• Everything
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• #### The Rotation Number for Quantum Integrable Systems

(2019)

For a two degree of freedom quantum integrable system, a new spectral quantity is defined, the quantum rotation number. In the semiclassical limit, the quantum rotation number can be detected on a joint spectrum and is shown to converge to the well-known classical rotation number. The proof requires not only semiclassical analysis (including Bohr-Sommerfeld quantization rules) but also a detailed study on how quantum labels can be assigned to the joint spectrum in a smooth way. This leads to the definition and analysis of asymptotic lattices. The general results are applied to the semitoric case where formulas become particularly natural.

• #### Analytic Bergman operators in the semiclassical limit

(2018)

Using a new quantization scheme, we construct approximate semi-classical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.

• #### On the stability of the Schwartz class under the magnetic Schrödinger flow

(2018)

We prove that the Schwartz class is stable under the magnetic Schrödinger flow when the magnetic 2-form is non-degenerate and does not oscillate too much at infinity.

• #### Long-time dynamics of coherent states in strong magnetic fields

(2018)

We consider a charged particle on a plane, subject to a strong, purely magnetic external field. It is well known that the quantum evolution closely follows the classical dynamics for short periods of time, while for times larger than $\ln \frac{1}{\hbar}$, where $\hbar$ is Planck’s constant, purely quantum phenomena are expected to happen. In this paper we investigate the Schrödinger evolution of generalized coherent states for times of order $1/\hbar$. We prove that, when the initial energy is low, the initial states splits into multiple wavepackets, each one following the average dynamics of the guiding center motion but at its own speed.

• #### Boundary effects on the magnetic Hamiltonian dynamics in two dimensions

(2018)

We study the Hamiltonian dynamics of a charged particle submitted to a pure magnetic field in a two-dimensional domain. We provide conditions on the magnetic field in a neighbourhood of the boundary to ensure the confinement of the particle. We also prove a formula for the scattering angle in the case of radial magnetic fields.

• #### Un monde d’oscillations — de l’horloge de Huygens à la physique quantique

Tangente 167 (2017)
• #### Les Annales Henri Lebesgue

Ann. H. Lebesgue 0 pp. 1-6 (2017)
• #### Integrable systems, symmetries, and quantization

Lett. Math. Phys. 108 (3) pp. 499-571 (2017)

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterpart are also presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can one recover the classical system?

• #### The affine invariant of generalized semitoric systems

Nonlinearity 30 (11) (2017)
• #### Magnetic Wells in dimension three

Anal. & PDE 9 (7) pp. 1575-1608 (2016)
• #### Spectral limits of semiclassical commuting self-adjoint operators

A mathematical tribute to Professor José María Montesinos Amilibia pp. 527-546 Dep. Geom. Topol. Fac. Cien. Mat. UCM, Madrid (2016)

Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint image of the principal symbols, in the semiclassical limit. This includes Berezin-Toeplitz quantization and certain cases of ℏ-pseudodifferential quantization, for instance when the symbols are uniformly bounded, and extends a result by L. Polterovich and the authors. In the last part of the paper we review the recent solution to the inverse problem for quantum integrable systems with periodic Hamiltonians, and explain how it also follows from the main result in this paper.

• #### Sharp symplectic embeddings of cylinders

Indag. Math. 27 (1) pp. 307-317 (2016)
• #### Inverse spectral theory for semiclassical Jaynes-Cummings systems

Math. Ann. 364 (3) pp. 1393-1413 (2016)

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 physicists and mathematicians such as the Jaynes-Cummings model (1963), which describes a two-level atom interacting with a quantized mode of an optical cavity, and more generally the so-called systems of Jaynes-Cummings type. In this paper we consider the joint spectrum of a pair of commuting semiclassical operators forming a quantum integrable system of Jaynes-Cummings type. We prove, assuming the Bohr-Sommerfeld rules hold, that if the joint spectrum of two of these systems coincide up to O(ℏ²), then the systems are isomorphic.

• #### Geometry and spectrum in 2D magnetic wells

Ann. Inst. Fourier 65 (1) pp. 137-169 (2015)
• #### Fiber connectivity and bifurcation diagrams for almost toric systems

Journal of Symplectic Geometry 13 (2015)
• #### Asymptotic Analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson Normal Form

Asymptotic Analysis 85 pp. 1-28 (2013)
• #### Microlocal Normal Forms for the Magnetic Laplacian

Journées EDP (2014)
• #### Semiclassical inverse spectral theory for singularities of focus-focus type

Commun. Math. Phys. 329 (2) pp. 809-820 (2014)
• #### Smooth normal forms for integrable Hamiltonian systems near a focus–focus singularity

Acta Math. Viet. 38 (1) (2013)
• #### Semiclassical quantization and spectral limits of $\hslash$-pseudodifferential and Berezin-Toeplitz operators

Proc. Lond. Math. Soc. (3) 109 (3) pp. 676-696 (2014)
• #### Hofer’s question on intermediate symplectic capacities

Proc. London Math. Soc (2015)

(2012)
• #### De l’autre côté du miroir... Le Spectre

Image des maths (2013)
• #### Isospectrality for Quantum Toric Integrable Systems

Ann. Sci. École Norm. Sup. 43 pp. 815-849 (2013)
• #### First steps in symplectic and spectral theory of integrable systems

Discrete Contin. Dyn. Syst. 32 (10) pp. 3325-3377 (2012)
• #### Hamiltonian dynamics and spectral theory for spin-oscillators

Comm. Math. Phys. 309 (1) pp. 123-154 (2012)
• #### Spectral invariants for coupled spin-oscillators

Séminaire X-EDP (2011)
• #### Remembering Johannes J. Duistermaat

Notices AMS 58 (06) (2011)
• #### Johannes Jisse (dit Hans) Duistermaat

Gazette des mathématiciens 127 (2011)
• #### Symplectic theory of completely integrable Hamiltonian systems

Bull. Amer. Math. Soc. (N.S.) 48 (3) pp. 409-455 (2011)
• #### Constructing integrable systems of semitoric type

Acta Math. 206 pp. 93-125 (2011)
• #### Semitoric integrable systems on symplectic 4-manifolds

Invent. Math. 177 (3) pp. 571-597 (2009)
• #### Symplectic inverse spectral theory for pseudodifferential operators

Progr. Math. 292 pp. 353-372 Birkhäuser/Springer, New York (2011)
• #### Symplectic invariants near hyperbolic-hyperbolic points

Regular & Chaotic Dyn 12 (6) pp. 689-716 (2007)
• #### Spectral asymptotics via the semiclassical Birkhoff normal form

Duke Math. J. 143 (3) pp. 463-511 (2008)
• #### Quantum Birkhoff normal form and semiclassical analysis

Adv. Studies in Pure Math. Mathematical Society of Japan (2009)
• #### Diophantine tori and spectral asymptotics for non-selfadjoint operators

Amer. J. Math. 169 (1) pp. 105-182 (2007)
• #### A Singular Poincaré Lemma

Int. Math. Res. Not. 2005 (1) pp. 27-45 (2005)

(2003)
• #### Symplectic techniques for semiclassical completely integrable systems

Topological methods in the theory of integrable systems pp. 241-270 Camb. Sci. Publ., Cambridge (2006)
• #### Moment polytopes for symplectic manifolds with monodromy

Adv. in Math. 208 pp. 909-934 (2007)
• #### Vanishing twist near focus-focus points

Nonlinearity 17 (5) pp. 1777-1785 (2004)
• #### Sign of the monodromy for Liouville integrable systems

Annales Henri Poincaré 3 (5) pp. 883-894 (2002)
• #### The Quantum Birkhoff Normal Form and Spectral Asymptotics

Journées EDP CNRS (2006)
• #### Invariants symplectiques et semi-classiques des systèmes intégrables avec singularités

Séminaire X-EDP (2001)
• #### On semi-global invariants for focus-focus singularities

Topology 42 (2) pp. 365-380 (2003)
• #### Quantum Monodromy and Bohr–Sommerfeld Rules

Letters in Mathematical Physics 55 (3) pp. 205-217 Kluwer Academic Publishers (2001)
• #### Singular Bohr-Sommerfeld rules for 2D integrable systems

Ann. Sci. École Norm. Sup. (4) 36 pp. 1-55 (2003)
• #### Quantum monodromy in integrable systems

Commun. Math. Phys. 203 (2) pp. 465-479 (1999)
• #### Formes normales semi-classiques des systèmes complètement intégrables au voisinage d’un point critique de l’application moment

Asymptotic Analysis 24 (3,4) pp. 319-342 (2000)
• #### Bohr-Sommerfeld conditions for Integrable Systems with critical manifolds of focus-focus type

Comm. Pure Appl. Math. 53 (2) pp. 143-217 (2000)
• #### Sur le spectre des systèmes complètement intégrables semi-classiques avec singularités

Institut Fourier, Université Grenoble 1 (1998)
• #### La recherche mathématique aux Pays-Bas

TechnoPol’der (1998)
• #### Indices de difféomorphismes de contact: exemple du tore en dimension 3

Ecole Normale Supérieure Paris / UC Berkeley / Univ. Paris XI (1994)
• #### Mémoire de magistère

École Normale Supérieure (Ulm) (1995)
• #### Systèmes intégrables semi-classiques: du local au global

Panoramas et Synthèses SMF (2006)
• #### Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics

• V. Matveev
• E. Miranda
• V. Roubtsov
• S. Tabashnikov
• S. Vũ Ngọc
Journal of Geometry and Physics 87 Elsevier (2015)