184 TIME DEPENDENT AND NONLINEAR POINT INTERACTIONS RODOLFO FIGARI Dipartimento di Scienze Fisich... more 184 TIME DEPENDENT AND NONLINEAR POINT INTERACTIONS RODOLFO FIGARI Dipartimento di Scienze Fisiche, Universita di Napoli" Federico II", Italy ... 1 Introduction Driven by new results obtained by S. Albeverio, R. Hoegh-Krohn, H. Holden, F. Gesztesy, M. Mebkhout, ...
We consider the Schrödinger equation in with nonlinearity concentrated in a finite set of points.... more We consider the Schrödinger equation in with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions.On considère l'équation de Schrödinger avec une nonlinéarité concentrée en un nombre fini de points. On formule le problème dans l'espace V d'énergie finie, qui contient strictement l'espace standard H1, à cause de la singularité spécifique des solutions. On prouve des résultats d'existence locale et même, pour une nonlinéarité répulsive ou faiblement attractive, l'existence globale des solutions.
Journal of Physics a Mathematical and General, Jul 13, 2004
We consider a quantum system of two particles in dimension three interacting via a smooth potenti... more We consider a quantum system of two particles in dimension three interacting via a smooth potential. We characterize the asymptotic dynamics in the limit of small mass ratio for an initial state given in product form, with an explicit control of the error. An application to the decoherence effect produced on the heavy particle is also discussed.
We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of poin... more We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V , which is strictly larger than the standard H 1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions. 2003 Éditions scientifiques et médicales Elsevier SAS
184 TIME DEPENDENT AND NONLINEAR POINT INTERACTIONS RODOLFO FIGARI Dipartimento di Scienze Fisich... more 184 TIME DEPENDENT AND NONLINEAR POINT INTERACTIONS RODOLFO FIGARI Dipartimento di Scienze Fisiche, Universita di Napoli" Federico II", Italy ... 1 Introduction Driven by new results obtained by S. Albeverio, R. Hoegh-Krohn, H. Holden, F. Gesztesy, M. Mebkhout, ...
We consider the Schrödinger equation in with nonlinearity concentrated in a finite set of points.... more We consider the Schrödinger equation in with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions.On considère l'équation de Schrödinger avec une nonlinéarité concentrée en un nombre fini de points. On formule le problème dans l'espace V d'énergie finie, qui contient strictement l'espace standard H1, à cause de la singularité spécifique des solutions. On prouve des résultats d'existence locale et même, pour une nonlinéarité répulsive ou faiblement attractive, l'existence globale des solutions.
Journal of Physics a Mathematical and General, Jul 13, 2004
We consider a quantum system of two particles in dimension three interacting via a smooth potenti... more We consider a quantum system of two particles in dimension three interacting via a smooth potential. We characterize the asymptotic dynamics in the limit of small mass ratio for an initial state given in product form, with an explicit control of the error. An application to the decoherence effect produced on the heavy particle is also discussed.
We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of poin... more We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V , which is strictly larger than the standard H 1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions. 2003 Éditions scientifiques et médicales Elsevier SAS
[English]: This proceedings e-book contains papers presented at the national Symposium on “Electr... more [English]: This proceedings e-book contains papers presented at the national Symposium on “Electronic Books and the practices of scholarly research”, held in Naples, Italy, on 20 June 2003. The advent of new technologies, tools, and digital resources is changing how scholars conduct their work, keep updated in their field or fields of study, and think about research. Moving from the reconstruction of the market of scientific communication, copyright policies, and management of long-term conservation strategies, the published papers aim to discuss the ways in which scholarly practices have changed in the last decades, even since the end of the last century, in teaching and in research, in various disciplines like history, phisics and biomedical sciences. / [Italiano]: Il volume raccoglie gli atti del convegno "I libri elettronici. Pratiche della didattica e della ricerca", organizzato il 20 giugno 2003, presso l’Università degli Studi di Napoli Federico II, con l’intendimento di chiarire quali vincoli e quali opportunità scaturiscano dallo sviluppo delle reti telematiche e dell’editoria elettronica per il prodotto culturale “libro” e, soprattutto, per la “monografia di ricerca”, ritenuta, da più di un secolo e mezzo, il veicolo di diffusione dei risultati della ricerca scientifica più compiutamente rispondente alle esigenze metodologiche e argomentative proprie delle scienze umane e sociali. Nella prima parte, il volume muove dalla precisa ricostruzione dei condizionamenti del mercato sui circuiti della comunicazione scientifica (G. Vitiello), e dalle loro ripercussioni sullo sviluppo normativo del copyright (A. De Robbio), per dedicare poi spazio all’analisi delle strategie di conservazione delle memorie digitali, un tema troppo spesso sottovalutato dalle istituzioni di ricerca e dai governi nazionali (M. Guercio). Nella seconda parte, è affrontato il problema dell’uso didattico degli e-book (G. Roncaglia), prima di passare ad analizzare e a valorizzare le possibilità che l’informatica e le reti telematiche sembrano aprire al variegato universo delle “pratiche disciplinari”, dalle scienze fisiche (R. Figari) e biomediche (M. Della Seta) agli studi storici (R. Delle Donne). Di primo acchito, i contributi riservati alle scienze biomediche, fisiche e storiche sembrano percorrere strade fortemente divergenti e rispondenti alla radicale diversità degli scopi e dei metodi propri delle tre discipline. Eppure, a una lettura più attenta, non sfuggirà che proprio il “mutamento digitale” dell’ultimo decennio sembra aprire la strada a nuove convergenze, sollecitate dalla consapevolezza che la risposta alle distorsioni del mercato vada cercata nell’uso consapevole delle reti telematiche e delle loro potenzialità, da perseguire anche attraverso l’implementazione di piattaforme per pubblicare, in formato elettronico, ad accesso aperto, monografie e riviste, materiale scientifico, didattico e multimediale.
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