混沌腔的电容和电荷弛豫电阻--随机矩阵Laguerre系综中两个线性统计量的联合分布
Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
摘要：
研究了由相干混沌腔和顶栅组成的量子RC电路中的交流输运。在随机矩阵方法中，我们研究了介观电容$C_μ=(1/C+1/C_q)^{-1}$和电荷弛豫电阻$R_q$的联合分布，其中$C$是几何电容，$C_q$是量子电容。我们用库仑气体方法研究了大量导电沟道$N$的极限。我们得到$\langle R_q\rangle\simeq h/(Ne^2)=R_\mathrm{dc}$和表明，相对波动的顺序$1/N$都为$C_q$和$R_q$，具有强相关性$\langle δC_qδR_q\rangle/\sqrt{\langle δC_q^2\rangle\,\langle δR_q^2\rangle}\simeq+0.707$。大偏差的详细分析涉及库仑气体中的二级相变。得到了二维相图。
英文摘要：
We consider the AC transport in a quantum RC circuit made of a coherent chaotic cavity with a top gate. Within a random matrix approach, we study the joint distribution for the mesoscopic capacitance $C_μ=(1/C+1/C_q)^{-1}$ and the charge relaxation resistance $R_q$, where $C$ is the geometric capacitance and $C_q$ the quantum capacitance. We study the limit of a large number of conducting channels $N$ with a Coulomb gas method. We obtain $\langle R_q\rangle\simeq h/(Ne^2)=R_\mathrm{dc}$ and show that the relative fluctuations are of order $1/N$ both for $C_q$ and $R_q$, with strong correlations $\langle δC_qδR_q\rangle/\sqrt{\langle δC_q^2\rangle\,\langle δR_q^2\rangle}\simeq+0.707$. The detailed analysis of large deviations involves a second order phase transition in the Coulomb gas. The two dimensional phase diagram is obtained.
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