Semiclassical Propagation of Coherent States for the Hartree Equation

TY - JOUR

T1 - Semiclassical Propagation of Coherent States for the Hartree Equation

AU - Athanassoulis, Agissilaos

AU - Paul, Thierry

AU - Pezzotti, Federica

AU - Pulvirenti, Mario

N1 - cited By 4

PY - 2011/12

Y1 - 2011/12

N2 - In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in L2 by ε being the Planck constant. Finally we present a full formal asymptotic expansion. © 2011 Springer Basel AG.

AB - In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in L2 by ε being the Planck constant. Finally we present a full formal asymptotic expansion. © 2011 Springer Basel AG.

U2 - 10.1007/s00023-011-0115-2

DO - 10.1007/s00023-011-0115-2

M3 - Article

SN - 1424-0661

VL - 12

SP - 1613

EP - 1634

JO - Annales Henri Poincaré

JF - Annales Henri Poincaré

IS - 8

ER -