caa a22 4500 467891508 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-005-9010-x doi (NATIONALLICENCE)springer-10.1007/s10955-005-9010-x Some Considerations on the Derivation of the Nonlinear Quantum Boltzmann Equation II: The Low Density Regime [Elektronische Daten] [D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti] In this paper we analyse the asymptotic dynamics of a system of N identical quantum particles in a low-density regime. Our approach follows the strategy introduced by the authors in a previous work,(2) to treat the simpler weak coupling regime. The time evolution of the Wigner transform of the one-particle reduced density matrix is represented by means of a perturbative series. The expansion is obtained upon iterating the Duhamel formula, in the spirit of the paper by Lanford.(32) For short times and small interaction potential, we rigorously prove that a subseries of the complete perturbative series, converges to the solution of the nonlinear Boltzmann equation that is physically relevant in the context. An important point is that we completely identify the cross-section entering the limiting Boltzmann equation, as being the Born series expansion of quantum scattering. As in ref. 2, our convergence result is only partial, in that we merely characterize the asymptotic behaviour of a subseries of the complete original perturbative expansion. We only have plausibility arguments in the direction of proving that the terms we neglect, when going from the original series to its associated subseries, are indeed vanishing in the limit. The present study holds in any dimension d ≥ 3. Springer Science + Business Media, Inc., 2006 Benedetto D. Dipartimento di Matematica, Università di Roma ‘La Sapienza', P.le Aldo Moro 5, 00185, Roma, Italy aut Castella F. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes, Cedex, France aut Esposito R. Diparmimento di Matematica pura ed applicata, Università di L'Aquila, Coppito, 67100, L'Aquila, France aut Pulvirenti M. Dipartimento di Matematica, Università di Roma ‘La Sapienza', P.le Aldo Moro 5, 00185, Roma, Italy aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 951-996 0022-4715 124:2-4<951 2006 124 10955 https://doi.org/10.1007/s10955-005-9010-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-9010-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Benedetto D. Dipartimento di Matematica, Università di Roma ‘La Sapienza', P.le Aldo Moro 5, 00185, Roma, Italy aut NATIONALLICENCE 700 1- Castella F. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes, Cedex, France aut NATIONALLICENCE 700 1- Esposito R. Diparmimento di Matematica pura ed applicata, Università di L'Aquila, Coppito, 67100, L'Aquila, France aut NATIONALLICENCE 700 1- Pulvirenti M. Dipartimento di Matematica, Università di Roma ‘La Sapienza', P.le Aldo Moro 5, 00185, Roma, Italy aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 951-996 0022-4715 124:2-4<951 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 467891508 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer