Miguel Escobar Azor, Léa Brooke, Stefano Evangelisti, Thierry Leininger, Pierre-François Loos, Nicolas Suaud, J. A. Berger
SciPost Phys. Core 1, 001 (2019) ·
published 11 November 2019
In this work we investigate Wigner localization at very low densities by
means of the exact diagonalization of the Hamiltonian. This yields numerically
exact results. In particular, we study a quasi-one-dimensional system of two
electrons that are confined to a ring by three-dimensional gaussians placed
along the ring perimeter. To characterize the Wigner localization we study
several appropriate observables, namely the two-body reduced density matrix,
the localization tensor and the particle-hole entropy. We show that the
localization tensor is the most promising quantity to study Wigner localization
since it accurately captures the transition from the delocalized to the
localized state and it can be applied to systems of all sizes.
SciPost Phys. Core 1, 002 (2019) ·
published 22 November 2019
We consider the generalized hydrodynamics including the recently introduced
diffusion term for an initially inhomogeneous state in the Lieb-Liniger model.
We construct a general solution to the linearized hydrodynamics equation in
terms of the eigenstates of the evolution operator and study two prototypical
classes of initial states: delocalized and localized spatially. We exhibit some
general features of the resulting dynamics, among them, we highlight the
difference between the ballistic and diffusive evolution. The first one governs
a spatial scrambling, the second, a scrambling of the quasi-particles content.
We also go one step beyond the linear regime and discuss the evolution of the
zero momentum mode that does not evolve in the linear regime.