Memory preservation and cooperative shielding in complex quantum networks

• URL: http://arxiv.org/abs/2503.05655v2
• Date: Tue, 05 Aug 2025 17:48:31 GMT
• Title: Memory preservation and cooperative shielding in complex quantum networks
• Authors: Simone Ausilio, Fausto Borgonovi, Giuseppe Luca Celardo, Jorge Yago Malo, Maria Luisa Chiofalo,
• Abstract summary: We study the transport properties of a quantum network described by the paradigmatic XXZ Hamiltonian.<n>We show how long range interactions induce a memory preserving effects and strongly affect the spreading of the excitations.<n>We discuss the implications of these properties in biology-related problems, such as an application to Weber's law in neuroscience, and their implementation in specific quantum technologies via biomimicry.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Complex quantum networks are powerful tools in the modeling of transport phenomena, particularly for biological systems, and enable the study of emergent phenomena in many-body quantum systems. High connectivity and long range interactions induce strong constraints on the system dynamics. Here, we study the transport properties of a quantum network described by the paradigmatic XXZ Hamiltonian, with non-trivial graph connectivity and topology, and long-range interaction. We show how long range interactions induce a memory preserving effects and strongly affect the spreading of the excitations due to cooperative shielding. We describe the memory-preserving effect in all-to-all connected regular networks with distance-independent couplings. Indeed the memory of the number of initially injected excitations is preserved over long times, being encoded in the number of frequencies present in the dynamics. Interestingly, we find that memory-preserving effects occur also in less regular graphs, such as quantum networks with either power-law node connectivity or complex, small-world type, architectures. We discuss the implications of these properties in biology-related problems, such as an application to Weber's law in neuroscience, and their implementation in specific quantum technologies via biomimicry. We also show how the presence of long range interaction strongly affect the dynamics of the excitations in small-world networks and power law all-to-all coupled networks. Indeed due to cooperative shielding as the connectivity or the range of interaction increase the initial excitation spreads more slowly among the network and becomes strongly dependent on the initial conditions.

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