
N'est plus au Laboratoire.
DUPUY Lucien
Position : Doctorant
Team: Astrophysique Stellaire
lucien.dupuy

etu.umontpellier.fr
0467143508
Room: 28, Floor: 4, Build.: 13
Research Topics: - phys/phys.phys/phys.phys.phys-atm-ph
- phys/phys.phys/phys.phys.phys-chem-ph
- phys/phys.phys/phys.phys.phys-comp-ph
- phys/phys.qphy
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Last scientific productions :

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Coping with the node problem in resonant scattering simulations using quantum trajectories: an efficient and accurate combined analytical-numerical scheme 
Author(s): Dupuy L., Scribano Y.
(Article) Published:
The European Physical Journal. Special Topics, vol. 232 p.1871–1883 (2023)
DOI: 10.1140/epjs/s11734-023-00924-3
Abstract: We report an efficient approach to accurately and efficiently compute transmission probabilities in
resonant deep tunneling regime. Dynamical systems subjects to this phenomenon prove hard to
simulate numerically even with exact methods, which motivates new methodological developments
owing to the impact resonant phenomena have in several processes such as chemical reactions and
electronic transport. Our approach is based on the original reformulation of stationnary quantum
scattering as the propagation of a quantum trajectory in extended phase space. The present paper
discusses in detail the node problem occurring to the time-independent quantum trajectory method
in this very challenging situation, and introduces an efficient node-skipping scheme to circumvent
expensive numerical integration in their vicinity. We illustrate how this numerical extension allows
to treat all regimes of quantum tunneling with great versatility by comparison to existing approaches
of the litterature. The quantum trajectory thus represents a very promising tool for the study of
complex chemical reactions characterized by resonant tunneling effect.
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Making sense of transmission resonances and Smith lifetimes in one-dimensional scattering: the extended phase space quantum trajectory picture 
Author(s): Dupuy L., Parlant Gerard, Poirier Bill, Scribano Y.
(Article) Published:
Chemical Physics, vol. 572 p.111952 (2023)
DOI: 10.1016/j.chemphys.2023.111952
Abstract: Resonances are ubiquitous in a wide range of physical and chemical phenomena. Their impact on
quantum scattering processes renders their study as important as it can be puzzling. In this paper,
we illustrate the accuracy of a fully quantum, purely trajectory based reformulation of quantum
mechanics proposed by one of the authors (Poirier) to acquire insights on shape resonances through
direct and accurate computation of the diagonal elements of Smith’s lifetime matrix. This study also
generalizes the relationship between the quantum trajectory propagation time and the Eisenbud-
Wigner time delay—introduced in our previous publication[1] for symmetric potentials—to the
general case of asymmetric potential profiles. In addition, we show how the complex amplitudes of
the scattering matrix can be extracted from left- and right-incident quantum trajectories. Finally, we
demonstrate that extended phase space quantum trajectories not only recover S-matrix and quantum
time quantities, but they also provide their own picture of resonant phenomena, as dynamically
distinct events characterised by an integer number of closed orbits in the quantum phase space.
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Contribution de l’effet tunnel à la réactivité chimique: une
approche par trajectoire quantique
Author(s): Dupuy L. , Scribano Y.
Conference: RCTF 2022 (Bordeaux, FR, 2022-06-27)
Abstract: L’effet tunnel est incontournable pour parfaire notre compréhension de la
réactivité chimique. Permettant le passage de barrières de réaction
cinétiquement infranchissables, son rôle primordial dans les réactions à basse
température et pour l’échange d’éléments légers est bien connu. Cependant,
l’assomption selon laquelle il serait sans impact hors de ces cas de figure a
également été démentie ces dernières années: Ni l’échange d’éléments
chimiques plus lourds que l’hélium[1], ni les réactions à température ambiante
ne justifient de le négliger à priori[2]. Sa capacité à orienter la formation d’un
produit de réaction l’élève au rang de troisième voie de contrôle de la
réactivité, au même titre que les contrôles cinétique et thermodynamique[3].
De ce fait, il est nécessaire de disposer de méthodes numériques capables
de reproduire cet effet purement quantique avec précision. Or, les méthodes
approchées les plus couramment employées pour estimer la probabilité de
transmission, comme WKB[4], ne garantissent pas un résultat fiable
( notamment en cas d’effet tunnel résonant, ou dans le régime
deep tunneling ). L’utilisation de formules analytiques dérivées de potentiels
approchés[5], une autre méthode répandue pour incorporer une estimation de
l’effet tunnel, souffre également de son manque de précision. Si ces méthodes
sont si largement utilisées, c’est avant tout pour leur simplicité et leur faible
coût calculatoire.
L’objet de cette contribution est de présenter une méthode efficace pour
déterminer la probabilité de transmission le long d’un chemin de réaction de
manière exacte[6,7]. Issue d’un formalisme rigoureusement équivalent à
l’équation de Schrödinger stationnaire, cette approche remplace la
détermination des états de diffusion par la propagation d’une trajectoire dans
un espace des phases étendu[8,9]. La méthode et son efficacité seront
illustrées sur des systèmes modèles ainsi qu’une réaction d’intérêt pour
l’astrochimie[10].
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Resonant Tunneling in Chemistry from Quantum Trajectory Based Method
Author(s): Dupuy L. , Scribano Y., Parlant Gerard, Poirier Bill
Invited Conference: QAMTS 2022 (Canmore, Alberta, CA, 2022-05-15)
Abstract: Owing to its reactivity enhancing properties, quantum tunneling represents one of the
most crucial effects to account for in order to achieve accurate prediction of rate
constants for numerous chemical processes[1], even at ambient temperature[2]. Over
the years, efficient methods emerged to accurately reproduce quantum tunneling in
approximate atomistic simulations, with much progress being made on assessing the
multidimensional character of the optimal tunneling path[3]. However resonant
tunneling still proves to be a difficult phenomenon to characterize in the aforementioned
methodological framework. In this talk, we present a purely trajectory based[4]
approach of great accuracy and efficiency[5] applied to potential energy profiles subject
to resonant tunneling. The working equations are a set of first order ODEs for a
Hamiltonian in an extended phase space with respect to its classical analog. Trajectory
propagation time enjoys a close relationship with collision lifetime, allowing to directly
recover Smith's quantal time delay[6] at the energy of interest and thus giving further
insight into resonant phenomena[7]. Trajectories describing scattering states with a
reflection probability of nearly unity manifest strong destructive interference patterns,
resulting in a very arduous numerical integration. This is reminiscent of pathologic
numerical behavior encountered by the log-derivative approach in the deep tunneling
regime[8] and constitutes a specific form of the well-known « node problem »
encountered in Bohmian Dynamics[9]. To cope with the node problem, we propose an
efficient semi-analytic scheme allowing trajectories to bypass nodes without significant
loss of accuracy. As a result the method is a robust tool to analyse resonant reactive
scattering.
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Smolyak representations with absorbing boundary
conditions for reaction path Hamiltonian of reactive
scattering
Author(s): Scribano Y. , Dupuy L., Lauvergnat David
Invited Conference: Spectroscopy and Dynamics of Coupled Anharmonic Vibrations of Floppy Molecular Systems (Telluride, US, 2022-06-06)
Abstract: In this work, we present the efficient combination of Smolyak representations with time independent quantum mechanical approach using absorbing boundary conditions for the cumulative reaction probability calculations of a multidimensional reactive scattering problem. Our approach uses both kinds of Smolyak representations (finite basis and grid) which drastically reduces the size of the basis representation for the cumulative reaction operator. The cumulative reaction probability is thus obtained by solving the eigenvalue problem within the context of reaction path Hamiltonian using the compact Smolyak basis combined with an iterative Lanczos algorithm. Benchmark calculations are presented for reactive scattering models with a linear reaction coordinate and applied to a 25D model highlighting the efficiency of the present approach for multidimensional reactive processes.
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