Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields

Abstract

Using a new method [9] it is possible to derive mean field equations from the microscopic N-body Schrodinger evolution of interacting particles without using BBGKY hierarchies. Recently this method was used to derive the Hartree equation for singular interactions [4] and the Gross Pitaevskii equation without positivity condition on the interaction [10] where one had to restrict the scaling behaviour of the interaction. In this paper more general scalings shall be considered assuming positivity of the interaction.

arXiv comment65 pages

References in corpus (3)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
• Mean-Field Dynamics: Singular Potentials and Rate of Convergence

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• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• On Mean Field Limits for Dynamical Systems
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• Derivation of the Time Dependent Two Dimensional Focusing NLS Equation
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
• The NLS limit for bosons in a quantum waveguide
• A Central Limit Theorem in Many-Body Quantum Dynamics
• Derivation of Mean-field Dynamics for Fermions
• Effective evolution equations from many body quantum dynamics
• Dynamics of Sound Waves in an Interacting Bose Gas