| 1. |
- Gosson, Maurice de, et al.
(author)
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Symplectic Path Intersections and the Leray Index
- 2001
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Conference paper (peer-reviewed)abstract
- We define a Maslov index for symplectic paths by using the properties of Leray's index for pairs of Lagrangian paths. Our constructions are purely topological, and the index we define satisfies a simple system of five axioms. The fifth axiom establishes a relation between the spectral flow of a family of symmetric matrices and the Maslov index
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| 2. |
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| 3. |
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| 4. |
- Gosson, Maurice de, et al.
(author)
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The Maslov Index of Periodic Hamiltonian Orbits
- 2003
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In: Journal of Physics A. - Bristol : IOP. - 0305-4470 .- 1361-6447. ; 36:48, s. 615-622
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Journal article (peer-reviewed)abstract
- we study the Maslov index of the monodromy matrix of periodic Hamiltonian orbit, extending substantially results of other authors
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| 5. |
- de Gosson, Maurice, et al.
(author)
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Continuity Properties for Born-Jordan Operators with Symbols in Hörmander Classes and Modulation Spaces
- 2020
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In: Acta Mathematica Scientia. - : Springer. - 0252-9602 .- 1003-3998 .- 1572-9087. ; 40:6, s. 1603-1626
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Journal article (peer-reviewed)abstract
- We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hormander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.
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| 6. |
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| 7. |
- Gosson, Maurice de
(author)
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On the classical and quantum evolution of Lagrangian half-forms in phase space
- 1999
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In: ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE. - PARIS : GAUTHIER-VILLARS/EDITIONS ELSEVIER. - 0246-0211. ; , s. 547-573
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Journal article (peer-reviewed)abstract
- The local expressions of a Lagrangian half-form on a quantized Lagrangian submanifold of phase space are the wavefunctions of quantum mechanics. We show that one recovers Maslov's asymptotic formula for the solutions to Schrodinger's equation if one transports these half-forms by the flow associated with a Hamiltonian H. We then consider the case when the Hamiltonian flow is replaced by the flow associated with the Bohmian, and are led to the conclusion that the use of Lagrangian half-forms leads to a quantum mechanics on phase space. (C) Elsevier, Paris.
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| 8. |
- Gosson, Maurice de
(author)
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On the notion of phase in mechanics
- 2004
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In: Journal of Physics A. - BRISTOL : IOP PUBLISHING LTD. - 0305-4470 .- 1361-6447. ; , s. 7297-7314
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Journal article (peer-reviewed)abstract
- The notion of phase plays an essential role in both semiclassical and quantum mechanics. But what is exactly a phase, and how does it change with time? It turns out that the most universal definition of a phase can be given in terms of Lagrangian manifolds by exploiting the properties of the Poincare-Cartan form. Such a phase is defined, not in configuration space, but rather in phase-space and is thus insensitive to the appearance of caustics. Surprisingly enough, this approach allows us to recover the Heisenberg-Weyl formalism without invoking commutation relations for observables.
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| 9. |
- Gosson, Maurice de
(author)
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Phase Space Quantization and the Uncertainty Principle
- 2003
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In: Physics Letters : Section A. - NA : NA. - 0375-9601. ; 317:5-6, s. 365-369
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Journal article (peer-reviewed)abstract
- We replace the usual heuristic notion of quantum cell by that of 'quantum blob', which does not depend on the dimension of phase space. Quantum blobs, which are defined in terms of symplectic capacities, are canonical invariants. They allow us to prove an exact uncertainty principle for semiclassically quantized Hamiltonian systems. (C) 2003 Elsevier B.V. All rights reserved.
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| 10. |
- Gosson, Maurice de
(author)
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Symplectic quantam cells and Wigner and Husimi functions
- 2005
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In: Bulletin des Sciences Mathématiques. - : Elsevier. - 0007-4497 .- 1952-4773. ; 129:3, s. 211-226
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Journal article (peer-reviewed)abstract
- We propose a definition of quantum cells which is invariant under symplectic transformations. We use this notion to the study of positivity properties of the Wigner and Husimi functions, which allows us to precise and to improve known results. © 2004 Elsevier SAS. Tous droits réservés.
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