Quantum mereology and subsystems from the spectrum

• URL: http://arxiv.org/abs/2409.01391v1
• Date: Mon, 2 Sep 2024 17:42:16 GMT
• Title: Quantum mereology and subsystems from the spectrum
• Authors: Nicolas Loizeau, Dries Sels,
• Abstract summary: We show that decomposing a system into subsystems is equivalent to decomposing a spectrum into other spectra. We argue that the number of subsystems can be inferred from the spectrum itself. In local models, this information is encoded in finite size corrections to the Gaussian density of states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The minimal ingredients to describe a quantum system are a Hamiltonian, an initial state, and a preferred tensor product structure that encodes a decomposition into subsystems. We explore a top-down approach in which the subsystems emerge from the spectrum of the whole system. This approach has been referred to as quantum mereology. First we show that decomposing a system into subsystems is equivalent to decomposing a spectrum into other spectra. Then we argue that the number of subsystems (the volume of the system) can be inferred from the spectrum itself. In local models, this information is encoded in finite size corrections to the Gaussian density of states.

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