两体和三体相互作用下的量子次扩散
Quantum subdiffusion with two- and three-body interactions
摘要：
我们研究了在弱无序一维晶格中存在二体和三体相互作用的少量子粒子云的动力学。这种相互作用极大地增强了非相互作用粒子的安德森局域化长度$ξ_1$。我们推出紧凑的波包，并表明，少体相互作用导致瞬态子扩散的波包，$m_2 \sim t^α$，$α<1$，超过$ξ_1$的长度尺度。次扩散指数与粒子数无关。二体相互作用产生两个和三个粒子的$α\approx0.5$，而三体相互作用将其降低为$α\approx0.2$。膨胀波包的尾部表现出指数缓慢下降的指数局域化。我们将我们的结果在非线性随机晶格的子扩散，并限制扩散在高维空间，如梳状晶格的结果。
英文摘要：
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 $ξ_1$ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, $m_2 \sim t^α$, $α<1$, on length scales beyond $ξ_1$. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield $α\approx0.5$ for two and three particles, while three-body interactions decrease it to $α\approx0.2$. 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.
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