Localization and « classical entanglement » in the discrete non-linear Schrödinger equation
Martina Giachello (GSSI, L’Aquila)
In this talk we present a detailed numerical study of the very peculiar thermodynamic properties of the localized high-energy phase of the Discrete Non-Linear Schrödinger Equation (DNLSE). A numerical ampling 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 « 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 thereforecalled Sent, grows with the system size N in the localized phase as Sent(N) ~ 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 « 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.