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 zbMATH or 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.

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• #### The inverse spectral problem for quantum semitoric systems

(2021)

We prove that semitoric systems are completely spectrally determined : from the joint spectrum of a quantum semitoric system, in the semiclassical limit, one can recover all symplectic invariants of the underlying classical semitoric system, and hence the isomorphism class of the system. Moreover, by using specific algorithms and formulas, we obtain a constructive way of computing the invariants from the spectrum.

• #### Magnetic WKB constructions on surfaces

Reviews in Mathematical Physics (2021)

This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumption that the magnetic field has a unique and non-degenerate minimum, we construct the local complex WKB approximations for eigenfunctions on a general surface. Furthermore, in the case of the Euclidean plane, with a radially symmetric magnetic field, the eigenfunctions are approximated in an exponentially weighted space.

• #### Uniform spectral asymptotics for semiclassical wells on phase space loops

Indag. Math. 32 (1) pp. 3-32 (2021)

We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which gives uniform eigenvalue asymptotics in a window $(−∞, b_0 + \varepsilon)$ for $\varepsilon>0$ independent on the semiclassical parameter. These asymptotics are obtained in two complementary settings: either an approximate invariance of the system under translation along the curve, which produces oscillating eigenvalues, or a Morse hypothesis reminiscent of Helffer-Sjöstrand’s “miniwell” situation.

• #### Spatio-temporal simulation of Covid-19 propagation via continuous automata

(2020)

We present a new continuous automata based computer simulation of virus propagation in human populations, and apply it to the Covid-19 outbreak, in various scales and situations. We also take the opportunity to propose various mathematical questions, and ask about their biological relevance.

• #### Quantum footprints of Liouville integrable systems

Reviews in Mathematical Physics 31 (1) pp. 2060014 (2021)

We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labellings of asymptotic lattices.

• #### Exponential localization in 2D pure magnetic wells

Arkiv för Matematik (2021)

We establish a magnetic Agmon estimate in the case of a purely magnetic single non-degenerate well, by means of the Fourier-Bros-Iagolnitzer transform and microlocal exponential estimates à la Martinez-Sjöstrand.

• #### Correction to: Inverse spectral theory for semiclassical Jaynes–Cummings systems

Mathematische Annalen 375 (1) pp. 917-920 (2019)

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 slightly weaker version of it.

• #### 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

Duke Math. J. 169 (16) pp. 3033-3097 (2020)

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical 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 $\CM^n$ 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

Math. Research Letters 27 (1) pp. 1-18 (2020)

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

Amer. J. Math. (2021)

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

Enseign. Math. 64 (3-4) pp. 353-369 (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) pp. 3993-4028 (2017)
• #### Magnetic Wells in dimension three

Anal. & PDE 9 (7) pp. 1575-1608 (2016)

This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit three semiclassical scales and their corresponding effective quantum Hamiltonians, by means of three microlocal normal forms *à la Birkhoff*. As a consequence, when the magnetic field admits a unique and non degenerate minimum, we are able to reduce the spectral analysis of the low-lying eigenvalues to a one-dimensional $\hbar$-pseudo-differential operator whose Weyl’s symbol admits an asymptotic expansion in powers of $\hbar^{\frac1 2}$.

• #### Spectral limits of semiclassical commuting self-adjoint operators

A mathematical tribute to Professor José Marı́a 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)

This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in $\mathbb{R}^2$. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional Hamiltonians. As a corollary, recent results by Helffer-Kordyukov are extended to higher energies.

• #### Fiber connectivity and bifurcation diagrams for almost toric systems

Journal of Symplectic Geometry 13 (2) pp. 343-386 (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)

We prove, assuming that the Bohr-Sommerfeld rules hold, that the joint spectrum near a focus-focus singular value of a quantum integrable system determines the classical Lagrangian foliation around the full focus-focus leaf. The result applies, for instance, to $\hbar$-pseudodifferential operators on cotangent bundles and Berezin-Toeplitz operators on prequantizable compact symplectic manifolds.

• #### 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)