Interaction-Enabled Hartree Fixed Points in Fermionic Resetting Dynamics

• URL: http://arxiv.org/abs/2603.15554v1
• Date: Mon, 16 Mar 2026 17:14:08 GMT
• Title: Interaction-Enabled Hartree Fixed Points in Fermionic Resetting Dynamics
• Abstract summary: In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are recoupled between interactions.<n>This provides a versatile route to engineer nonequilibrium states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in fermionic models.<n>We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are reinitialized between interactions. This provides a versatile route to engineer nonequilibrium steady states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in quadratic fermionic models. The baseline noninteracting resetting scheme yields an affine evolution for the subsystem single-particle density matrix (SPDM), with a clear operational interpretation: a finite environment block E mediates the interaction between the subsystem S and an ideal external thermal reservoir. In this work, we develop a controlled extension of such a framework to weakly interacting systems. We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior. We further construct a completely positive (CP-safe) Gaussian Lindblad embedding that reproduces the resetting dynamics in the noninteracting limit and yields a continuous-time representation of environmental thermalization when interactions are present. Our analytical results are complemented by numerical studies of a ring segmentation geometry and a minimal two-site model, revealing interaction-enabled steady states that cannot be obtained in any purely quadratic setting. Together, these results establish a general and physically consistent route for incorporating weak interactions ino resetting-based approaches to open quantum system.

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