Derivation of the time-dependent Hartree equations for strongly interacting dense fermionic systems

2025/07/16 by Hoang, Duc Viet, Mitrouskas, David, Pickl, Peter
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.12390

Abstract

The time-dependent Hartree and Hartree-Fock equations provide effective mean-field descriptions for the dynamics of large fermionic systems and play a fundamental role in many areas of physics. In this work, we rigorously derive the time-dependent Hartree equations as the large-N limit of the microscopic Schrödinger dynamics of N fermions confined to a volume of order one and interacting via strong pair potentials. A central step in our analysis is the implementation of time-dependent gauge transformations, which eliminate the dominant contribution from the interaction potential in both the Schrödinger and Hartree evolutions.

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