具有弱集中吸收体的随机力场中的一维经典扩散
One-dimensional classical diffusion in a random force field with weakly concentrated absorbers
摘要：
研究了具有弱吸收体浓度$ρ$的随机力场中的一维经典扩散模型。力场被视为高斯白噪声与$\mean{ϕ(x)}=0$和$\mean{ϕ(x)ϕ(x')}=g δ(x-x')$。我们的分析依赖于Fokker-Planck算子和量子哈密顿量之间的关系，其中吸收导致超对称性破缺。使用Lifshits参数，它表明，平均返回概率是一个幂律$\smean{P(x,t|x,0)}\sim{}t^{-\sqrt{2ρ/g}}$（与通常的Lifshits指数衰减$\exp{-(ρ^2t)^{1/3}}$在没有随机力场）。讨论了量子哈密顿量的局域化性质。
英文摘要：
A one-dimensional model of classical diffusion in a random force field with a weak concentration $ρ$ of absorbers is studied. The force field is taken as a Gaussian white noise with $\mean{ϕ(x)}=0$ and $\mean{ϕ(x)ϕ(x')}=g δ(x-x')$. Our analysis relies on the relation between the Fokker-Planck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument, it is shown that the average return probability is a power law $\smean{P(x,t|x,0)}\sim{}t^{-\sqrt{2ρ/g}}$ (to be compared with the usual Lifshits exponential decay $\exp{-(ρ^2t)^{1/3}}$ in the absence of the random force field). The localisation properties of the underlying quantum Hamiltonian are discussed as well.
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