The Experts below are selected from a list of 31749 Experts worldwide ranked by ideXlab platform
F Borondo - One of the best experts on this subject based on the ideXlab platform.
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deep learning methods for the computation of vibrational waveFunctions
Communications in Nonlinear Science and Numerical Simulation, 2021Co-Authors: Laia Domingo, F BorondoAbstract:Abstract In this paper, we design and use two Deep Learning models to generate the ground and excited waveFunctions of different Hamiltonians suitable for the study of the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions and ask the network to generalize these solutions to more complex Hamiltonian Functions. Since the Hamiltonians solutions used to train the neural networks are computationally cheap, the training process is fast and efficient. This approach allows to reproduce the excited vibrational waveFunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical model of the system. This makes this approach versatile and can be used in the study of multiple systems in quantum chemistry.
Fairon Maxime - One of the best experts on this subject based on the ideXlab platform.
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On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
'Springer Science and Business Media LLC', 2020Co-Authors: Chalykh Oleg, Fairon MaximeAbstract:We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh’s formalism, we construct commuting Hamiltonian Functions on the phase space and identify one of the flows with the spin Ruijsenaars–Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly
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On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
'Springer Science and Business Media LLC', 2020Co-Authors: Chalykh Oleg, Fairon MaximeAbstract:We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh's formalism, we construct commuting Hamiltonian Functions on the phase space and identify one of the flows with the spin Ruijsenaars-Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly.Comment: 30 pages. v2: improved exposition in Section 3.1, added Remarks 5.6 and 5.7. v3: References added, accepted versio
Laia Domingo - One of the best experts on this subject based on the ideXlab platform.
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deep learning methods for the computation of vibrational waveFunctions
Communications in Nonlinear Science and Numerical Simulation, 2021Co-Authors: Laia Domingo, F BorondoAbstract:Abstract In this paper, we design and use two Deep Learning models to generate the ground and excited waveFunctions of different Hamiltonians suitable for the study of the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions and ask the network to generalize these solutions to more complex Hamiltonian Functions. Since the Hamiltonians solutions used to train the neural networks are computationally cheap, the training process is fast and efficient. This approach allows to reproduce the excited vibrational waveFunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical model of the system. This makes this approach versatile and can be used in the study of multiple systems in quantum chemistry.
Chalykh Oleg - One of the best experts on this subject based on the ideXlab platform.
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On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
'Springer Science and Business Media LLC', 2020Co-Authors: Chalykh Oleg, Fairon MaximeAbstract:We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh’s formalism, we construct commuting Hamiltonian Functions on the phase space and identify one of the flows with the spin Ruijsenaars–Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly
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On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
'Springer Science and Business Media LLC', 2020Co-Authors: Chalykh Oleg, Fairon MaximeAbstract:We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh's formalism, we construct commuting Hamiltonian Functions on the phase space and identify one of the flows with the spin Ruijsenaars-Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly.Comment: 30 pages. v2: improved exposition in Section 3.1, added Remarks 5.6 and 5.7. v3: References added, accepted versio
Eduardo Martinez - One of the best experts on this subject based on the ideXlab platform.
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lagrangian submanifolds and dynamics on lie algebroids
Journal of Physics A, 2005Co-Authors: Manuel De Leon, Juan Carlos Marrero, Eduardo MartinezAbstract:In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) Functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) Functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange–Poincare (Hamilton–Poincare) equations are the Euler–Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange–Poincare (Hamilton–Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids.
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lagrangian submanifolds and dynamics on lie algebroids
arXiv: Differential Geometry, 2004Co-Authors: Manuel De Leon, Juan Carlos Marrero, Eduardo MartinezAbstract:In some previous papers, a geometric description of Lagrangian Mechanics on Lie algebroids has been developed. In the present paper, we give a Hamiltonian description of Mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits to deal with Lagrangian (Hamiltonian) Functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) Functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids.
