Discrete non-linear Schrödinger equation - Martina Giachello - Young Seminars SIFS скачать в хорошем качестве

Discrete non-linear Schrödinger equation - Martina Giachello - Young Seminars SIFS

Localization and ‘classical entanglement’ in the discrete non-linear Schrödinger equation Martina Giachello, Gran Sasso Science Institute (GSSI, L’Aquila) Abstract: 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 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 "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 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.