Applicability of mean-field theory for time-dependent open quantum systems with infinite-range interactions

• URL: http://arxiv.org/abs/2403.17163v1
• Date: Mon, 25 Mar 2024 20:24:30 GMT
• Title: Applicability of mean-field theory for time-dependent open quantum systems with infinite-range interactions
• Authors: Federico Carollo, Igor Lesanovsky,
• Abstract summary: We show that mean-field theory is applicable to time-dependent infinite-range interacting systems. We provide bounds for finite-size effects and their dependence on the evolution time.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows to induce and explore a plethora of nonequilibrium dynamical phases, including time-crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.

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