are random functions of $x$ in the region $0\le x\le L$ and zero elsewhere and consider two different random models. In Model I, we assume that $u$ and $a$ are [*independent*]{} random functions of $x$ and are given by $$\begin{aligned}
u=u_0+\delta u(x),~
a=a_0+\delta a(x),\end{aligned}$$ where $u_0$ and $a_0$ are the disorder-averaged values of $u$ and $a$ and $\delta u(x)$ and $\delta a(x)$ are Gaussian random functions satisfying $$\begin{aligned}
&&\langle\delta u(x)\delta u(x^\prime)\rangle={\tilde g_u}\delta(x-x^\prime),~~\langle\delta u(x)\rangle=0,\nonumber\\
&&\langle\delta a(x)\delta a(x^\prime)\rangle={\tilde g_a}\delta(x-x^\prime),~~\langle\delta a(x)\rangle=0.\end{aligned}$$ The notation $\langle\cdots\rangle$ denotes averaging over disorder and $\tilde g_u$ and $\tilde g_a$ are independent parameters characterizing the strength of disorder. In Model II, we consider the situation where the random functions $\delta u(x)$ and $\delta a(x)$ are not independent, but proportional to each other such that $$\begin{aligned}
\delta a(x)=f\delta u(x),\end{aligned}$$ where $f$ is a real constant. We point out that our vector potential configuration corresponds to the external magnetic field given by $$B_0(x)=\frac{\hbar k}{e}\left[a_0\delta(x)-a_0\delta(x-L)\right]+\delta B(x),$$ where $\delta B(x)$ is a random magnetic field fluctuating between positive and negative values with zero average. When $a_0$ is zero, we have a purely random magnetic field. A similar type of nonrandom models with two $\delta$ functions of opposite signs have been studied previously.[@agr] From 