Signatures of Anderson localization and delocalized random quantum states
arXiv:1803.02149 · doi:10.1016/j.chemphys.2018.03.006
Abstract
We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest model of a 1D disordered chain and we analyse both the dynamics of an initially localized state and the dynamics of quantum states drawn at random from the ensemble corresponding to the minimum knowledge about the initial state. While in the former case the site distribution remains confined in a limited portion of the chain, the site distribution of random pure state fluctuates around an equilibrium average that is delocalized over the entire chain. A clear connection between the equilibration observed when the system is initialized in a fully localized state and the amplitude of dynamical fluctuations of a typical random pure state is established.
References in corpus (31)
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Anderson localization of a non-interacting Bose-Einstein condensate
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Quantum thermalization through entanglement in an isolated many-body system
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Many-body localization in a quantum simulator with programmable random disorder
- Canonical Typicality
- Quantum mechanical evolution towards thermal equilibrium
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Ergodic dynamics and thermalization in an isolated quantum system
- Typicality for Generalized Microcanonical Ensembles
- Quantum equilibration in finite time
- Universal Spectral Correlations at the Mobility Edge
- Unitary equilibrations: probability distribution of the Loschmidt echo
- Time-resolved observation of thermalization in an isolated quantum system
- Equilibration time scales of physically relevant observables
- Localization of a matter wave packet in a disordered potential
- Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
- Pure state quantum statistical mechanics and black holes
- Typicality in Ensembles of Quantum States: Monte Carlo Sampling versus Analytical Approximations
- A generalized quantum microcanonical ensemble
- Geometry of quantum observables and thermodynamics of small systems
- Unitarity, ergodicity, and quantum thermodynamics
- Dynamics and (de)localization in a one-dimensional tight-binding chain
- Beyond quantum microcanonical statistics
- Localization of wave packets in one-dimensional random potentials
- Theory of temporal fluctuations in isolated quantum systems