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Quantum Dynamics and Spectral Analysis

Group “Classical and Quantum Dynamical Systems”

The research of the team Quantum Dynamics and Spectral Analysis is focused on development of mathematical methods for applications to problems in physics. In particular, our research pertains to diffusion and spectral properties of nanostructure models, of models in atomic physics or in quantum field theory, properties of the solutions of partial differential equations that occurs in physics, and unicity, stability and reconstruction in inverse problems.

Our main scientific activities are:
Nanostructures: Scattering properties of waves in optic fibres and in quantum wave guides; spectral properties of differential operators on graphs; gap opening at Fermi level and semiconductivity via periodic electrostatic gating in graphene samples ; Andreev reflection for SNS junctions in semiclassical limit.

PDE and inverse problems: Inverse problems for anomalous diffusion of time fractional equations of complex fluids, porous media, underground diffusion of polluting substances; inverse problems for characteristic coefficients (conductivity, absorption) in various diffusion or hyperbolic equations, with applications to wave guides, taxis-diffusion in angiogenesis problems, etc. Regularization of solutions in collisional kinetic theory, in particular the non cutoff Boltzmann equations.

Standard Model, QFT and atomic physics: Rigorous analysis of Hamiltonians in particle physics: nonperturbative quantum electrodynamics , spectral theory for weak interactions and muonic atoms , derivation of van der Waals-London law; Quantum field theory in de Sitter space; scattering theory for nonrelativistic models on static space-times; Localization/delocalization properties for random Schrödinger operators ; bulk and edge states for magnetic Schrödinger operators.

Part of our activity gives rise to international collaborations with the following institutions: Aalborg University, Pontificia Universidad Catolica de Chile, Karlsruhe Institute of Technology, Kyoto Institute of Technology, Metz University, Moscow Institute of Physics and Technology.

Directory of Members

Barbaroux Jean-Marie University faculty
Chef de l’équipe « Dynamique quantique et analyse spectrale »
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Boughanja Yosra PhD candidate
Briet Philippe University faculty
Référent site UTLN
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Gaïtan Patricia University faculty
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Hamza Abdou-Soimadou PhD candidate
Hartig Michael PhD candidate
Kian Yavar University faculty
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Leopold Elie University faculty
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M’Madi-Issimail Mohamed-Mouneime PhD candidate
Panati Annalisa University faculty
Pillet Claude-Alain University faculty
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Rouleux Michel University faculty
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Soccorsi Eric University faculty
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SOUSSI Yosra PhD candidate
Zalczer Sylvain PhD candidate

List of Publications

118 results
Journal article
C. Gérard, F. Hiroshima, A. Panati, A. Suzuki
Removal of UV cutoff for the Nelson model with variable coefficients
Letters in Mathematical Physics, Springer Verlag, 2012, 101 (3), pp.305-322. ⟨10.1007/s11005-012-0577-2⟩
Journal article
Horia D. Cornean, Pierre Duclos, Radu Purice
Adiabatic non-equilibrium steady states in the partition free approach
Annales Henri Poincaré, Springer Verlag, 2012, 13 (4), pp.827-856. ⟨10.1007/s00023-011-0144-x⟩
Conference paper
Jean-Michel Combes, François Germinet, Abel Klein
Lifshitz tails estimate for the density of states of the Anderson model
Spectra of Random Operators and Related Topics, Jul 2011, Kyoto University, Japan. pp.1-9
Book Section
Jacek Gilewicz, Radosław Jedynak
Compatibility of Continued Fraction Convergents with Padé Approximants
Walter Gautschi; Giuseppe Mastroianni; Themistocles M. Rassias. Approximation and Computation: In Honor of Gradimir V. Milovanovi, 42, Springer, pp.135-144, 2011, Springer Optimization and Its Applications, 978-1-4419-6593-6. ⟨10.1007/978-1-4419-6594-3_10⟩
Journal article
Walter H. Aschbacher, Jean-Marie Barbaroux, Jérémy Faupin, Jean-Claude Guillot
Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W±, II
Annales Henri Poincaré, Springer Verlag, 2011, 12 (8), pp.1539-1570. ⟨10.1007/s00023-011-0114-3⟩
Journal article
Annalisa Panati, Christian Gérard, Fumio Hiroshima, Akito Suzuki
Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime
RIMS Kokyuroku Bessatsu, 2010, B21, pp.015-024
Journal article
S. Yu. Dobrokhotov, M. Rouleux
The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2010, 87 (3), pp.430-435. ⟨10.1134/S0001434610030168⟩
Journal article
Jean-Marie Barbaroux, Thomas Chen, Vitali Vougalter, Semjon Vugalter
Quantitative estimates on the binding energy for Hydrogen in non-relativistic QED
Annales Henri Poincaré, Springer Verlag, 2010, 11 (8), pp.1487-1544. ⟨10.1142/S0129055X14500160⟩
Journal article
Elie Léopold
Asymptotic behaviours and general recurrence relations
Applied Numerical Mathematics, Elsevier, 2010, 60 (12), pp.1352-1363. ⟨10.1016/j.apnum.2010.08.001⟩
Journal article
Jacek Gilewicz
100 years of improvements of bounding properties of Padé approximants to the Stieltjes functions: One-point, two-point and N-point Padé approximants
Applied Numerical Mathematics, Elsevier, 2010, 60 (12), pp.1320-1331. ⟨10.1016/j.apnum.2010.05.007⟩
118 results