Quantum subdiffusion with two- and three-body interactions

Abstract

We study the dynamics of a few-quantum-particle cloud in the presence of two-and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m2 ∼ t α , α < 1, on length scales beyond ξ1. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.

Quantum dynamics of a $4π$-kink in Josephson junctions parallel arrays with large kinetic inductances

“…This procedure resembles a one elaborated previously for the analysis of two interacting quantum particles (e.g. bosons) moving on a one-dimensional periodic lattice [37,38].…”

Floquet Anderson localization of two interacting discrete time quantum walks

“…To assess TIW localization length scales we will project p ij in three different ways onto a one-dimensional coordinate space and compute the standard deviation of a probability distribution vector {v i } (see e.g. [21,22])…”

“…The challenging study of the interplay of interaction and disorder leads to a number of unexpected results for the localization properties of many particles eigenstates. The seemingly simplest case of two interacting particles (TIP) in one space dimension was analyzed in an impressive set of publications [10][11][12][13][14][15][16][17][18][19][20][21][22]. For uncorrelated disorder the TIP localization length ξ 2 is assumed to be finite, with the main questions addressing the way ξ 2 scales with ξ 1 in the limit of weak disorder [10][11][12][13][14][15][16][17][18][19][20], and the nature of the observed sub-diffusive wave packet spreading on length scales ξ 1 L ξ 2 [21,22].…”

Slow Thermalization of Few-Body Dipole-Dipole Interactions

“…While some recent work has shown that localiza-tion can persist in the presence of three-body interactions [60,61], most studies of thermalization to date focus on two-body interactions. Three-and four-body interactions have been observed in both cesium and rubidium [62][63][64][65].…”