We prove an abstract result giving a ⟨t⟩ℰ upper bound on the growth of the Sobolev norms of a time-dependent Schrödinger equation of the form iψ˙=H0ψ+V(t)ψ. {Here} H0 is assumed to be the Hamiltonian of a steep quantum integrable system and to be a {pseudodifferential} operator of order d>1 ; V(t) is a time-dependent family of pseudodifferential operators, unbounded, but of order b
Growth of Sobolev norms in quasi-integrable quantum systems / Bambusi, Dario; Langella, Beatrice. - In: ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE. - ISSN 0012-9593. - 582:4(2025), pp. 997-1035. [10.24033/asens.2623]
Growth of Sobolev norms in quasi-integrable quantum systems
LANGELLA, Beatrice
2025-01-01
Abstract
We prove an abstract result giving a ⟨t⟩ℰ upper bound on the growth of the Sobolev norms of a time-dependent Schrödinger equation of the form iψ˙=H0ψ+V(t)ψ. {Here} H0 is assumed to be the Hamiltonian of a steep quantum integrable system and to be a {pseudodifferential} operator of order d>1 ; V(t) is a time-dependent family of pseudodifferential operators, unbounded, but of order bFile in questo prodotto:
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