TY - JOUR
T1 - Derivation of the two-dimensional nonlinear schrödinger equation from many body quantum dynamics
AU - Kirkpatrick, Kay
AU - Schlein, Benjamin
AU - Staffilani, Gigliola
PY - 2011/2
Y1 - 2011/2
N2 - We derive rigorously, for both R2 and [-L, L] ×2, the cubic nonlinear Schr̈odinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cubic NLS; and then we prove uniqueness for the infinite hierarchy, which requires number-theoretical techniques in the periodic case.
AB - We derive rigorously, for both R2 and [-L, L] ×2, the cubic nonlinear Schr̈odinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cubic NLS; and then we prove uniqueness for the infinite hierarchy, which requires number-theoretical techniques in the periodic case.
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U2 - 10.1353/ajm.2011.0004
DO - 10.1353/ajm.2011.0004
M3 - Article
AN - SCOPUS:79251564808
SN - 0002-9327
VL - 133
SP - 91
EP - 130
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 1
ER -