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arXiv · 2507.12390

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

Duc Viet Hoang·David Mitrouskas·Peter Pickl
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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 Schr\"odinger 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 Schr\"odinger and Hartree evolutions.

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Duc Viet Hoang, David Mitrouskas, Peter Pickl. 2025-07-16. Derivation of the time-dependent Hartree equations for strongly interacting dense fermionic systems. https://arxiv.org/abs/2507.12390

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