Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
arXiv:2102.10298 · doi:10.1007/s10955-021-02870-7
Abstract
It is well known that, if the initial conditions have sufficiently high energy density, the dynamics of the classical Discrete Non-Linear Schrödinger Equation (DNLSE) on a lattice shows a form of breaking of ergodicity, with a finite fraction of the total charge accumulating on a few sites and residing there for times that diverge quickly in the thermodynamic limit. In this paper we show that this kind of localization can be attributed to some geometric properties of the microcanonical potential energy surface, and that it can be associated to a phase transition in the lowest eigenvalue of the Laplacian on said surface. We also show that the approximation of considering the phase space motion on the potential energy surface only, with effective decoupling of the potential and kinetic partition functions, is justified in the large connectivity limit, or fully connected model. In this model we further observe a synchronization transition, with a synchronized phase at low temperatures.
16+2 pages, 10 figures
References in corpus (18)
- Many-Body Physics with Ultracold Gases
- Many body localization and thermalization in quantum statistical mechanics
- Theoretical perspective on the glass transition and amorphous materials
- Localization of interacting fermions at high temperature
- Many-body localization edge in the random-field Heisenberg chain
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- Supercooled Liquids for Pedestrians
- Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
- Integrals of motion in the Many-Body localized phase
- Ergodicity breaking in a model showing many-body localization
- Many-body mobility edge in a mean-field quantum spin glass
- Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices
- Clustering of non-ergodic eigenstates in quantum spin glasses
- Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
- Finite-size localization scenarios in condensation transitions
- Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
- Entropic barriers as a reason for hardness in both classical and quantum algorithms
Cited by in corpus (6)
- Chaos and localization in the Discrete Nonlinear Schrödinger Equation
- Localization in boundary-driven lattice models
- Onsager coefficients in a coupled-transport model displaying a condensation transition
- Relaxation dynamics and finite-size effects in a simple model of condensation
- Infinite-temperature thermostats by energy localization in a nonequilibrium setup
- Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation