Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation

• URL: http://arxiv.org/abs/2503.14364v2
• Date: Fri, 17 Oct 2025 14:51:32 GMT
• Title: Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Authors: Martina Giachello, Stefano Iubini, Roberto Livi, Giacomo Gradenigo,
• Abstract summary: We study the peculiar thermodynamic properties of the localized high-energy phase of the Discrete Non-Linear Schr"odinger Equation (DNLSE)<n>A numerical sampling of the microcanonical ensemble done by means of Hamiltonian dynamics reveals a new and subtle relation between the presence of the localized phase and a property of the system.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We perform a detailed numerical study of the very peculiar thermodynamic properties of the localized high-energy phase of the Discrete Non-Linear Schr\"odinger Equation (DNLSE). A numerical sampling of the microcanonical ensemble done by means of Hamiltonian dynamics reveals a new and subtle relation between the presence of the localized phase and a property of the system that we have called {\it ``classical entanglement''}. Our main finding is that a quantity defined for our classical system in perfect analogy with the entanglement entropy of quantum ones, and that we have therefore called $S_{\mathrm{ent}}$, grows with the system size $N$ in the localized phase as $S_{\mathrm{ent}}(N) \sim \log(N)$, therefore revealing the presence of subtle non-local correlations between any finite portion of the system and the rest of it. This manifestation of {\it ``classical entanglement''} beautifully captures the lack of system separability in the DNLSE localized phase, revealing how statistical correlations specific to the microcanonical ensemble and non-reproducible in the canonical one, may concur to determine a property totally analogous to the one produced by non-local quantum correlations.

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