Rigorous Derivation of the Cubic NLS in Dimension One

By R. Adami, François Golse, A. Teta. 2007

158 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/85381cd83647e5085da2c1c3a594d44f60124734

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics (2007, methodology): “In [3, 5, 6], models described by the Hamiltonian HN = N∑ j=1 −∆xj + 1 N N∑ i j N3βV (Nβ(xi − xj)) with β ∈ (0, 1] with an N -dependent potential were considered (in the one-dimensional case, N -dependent potentials were considered by Adami, Golse and Teta in [1]).”
Effective Evolution Equations from Quantum Dynamics (2015, background): “Results in this direction have been obtained in [1, 2, 20] in the one-dimensional setting, in [42] in the two-dimensional case and in [27] in three dimensions.”
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems (2005, unknown): “Keywords: Feynman diagrams, BBGKY hierarchy, dispersive estimates, propagation of chaos.”
A Simple Derivation of Mean Field Limits for Quantum Systems (2009, background): “Derivations of such mean field equations from the microscopic N body Schrödinger evolution are usually done for the reduced one particle density and are naturally based on hierarchies [16, 3, 2, 4, 5, 1].”
Quantitative Derivation of the Gross‐Pitaevskii Equation (2012, background): “This general scheme, first introduced in [36] for bounded interactions, was later extended to more singular potentials; see, for example, [1,6, 9, 10, 12, 19, 27].”
Mean–Field Evolution of Fermionic Systems (2013, background): “As a consequence, the limiting Hartree equation has a local nonlinearity (nonlinear Schrödinger equations with local nonlinearity in one and two dimensions have been derived from many body quantum mechanics in appropriate mean field limits in [1, 31]).”