Transient and persistent particle subdiffusion in a disordered chain coupled to bosons

We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between dynamics due to noninteracting bosons and hard-core bosons. In the first case the transient dynamics is subdiffusive, but multiboson processes allow for long-time normal diffusion, while hard-core effects suppress multiboson processes leading to persistent subdiffusive transport, consistent with numerical results for a full many-body evolution. In contrast, analogous study for a quasiperiodic potential reveals a stable long-time diffusion.

Figure 1

(a) and (b) Integrated distributions of local rates $I\left({\mathrm{\Gamma }}_l\right)$ at different disorders $W$, for ${\omega }_0=g=1,t_b=0.4$ with full (continuous lines) and simplified (dashed lines) rates: (a) NB at $T=2$ and (b) HCB at $T\to \infty$. (c) Time evolution of the SP spread ${\sigma }^2\left(t\right)$ for NB at the same parameters, calculated via rate equations, (d) evolution of the full many-body system using the LHS method. Dot-dashed lines show the diffusion thresholds.

Figure 2

(a) Spread ${\sigma }^2\left(t\right)$, evaluated for HCB with parameters as in Fig. 1. (b) Corresponding averaged SP profile ${\overline{p}}_l\left(t\right)$, evaluated for fixed $t=50$, and for different $W=2-6$. (c) (Sub)diffusion exponents $\gamma$ vs disorder $W$ as evaluated from FGR, simplified rates (SFGR), and via full simulation using LHS, respectively. (d) $\gamma$ from the FGR approach for different ${\omega }_0=1.5,2.0$ and shorter $t<100$ compared with LHS results for ${\omega }_0=1$.

Figure 3

(a) Distribution $I\left({\mathrm{\Gamma }}_l\right)$ and (b) spread ${\sigma }^2\left(t\right)$ for HCB with the same parameters as in Fig. 1 but for quasiperiodic potential.