Quantum Dynamics with Mean Field Interactions: a New Approach

Abstract

We propose a new approach for the study of the time evolution of a factorized $N$-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the $N$-particle Schrödinger equation is shown to converge to the projection onto the one-dimensional subspace spanned by the solution to the Hartree equation with a speed of convergence of order 1/N for all fixed times.

11 pages

References in corpus (5)

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• Propagation of Correlations in Quantum Lattice Systems
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Cited by in corpus (25)

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• A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on ${\mathbb{T}}^3$ from the dynamics of many-body quantum systems
• Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data
• The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
• Beyond Bogoliubov Dynamics
• Randomization and the Gross-Pitaevskii hierarchy
• A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
• Towards Rigorous Derivation of Quantum Kinetic Equations
• Rate of Convergence Towards Semi-Relativistic Hartree Dynamics
• Quantum Kinetic Equations of Many-Particle Systems in Condensed States
• Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
• Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential
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• Proposal for a Lorenz qubit
• Protocol for nonlinear state discrimination in rotating condensate
• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• The universe as a nonlinear quantum simulation: Large $n$ limit of the central spin model