We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble of Random Matrix Theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form $<λ_1^m>$ for $m>-|N_1-N_2|-1$ and $β=2$, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation functions for $β=2,4$ which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants.
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 correlation…
We present an experimental study of missing level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis which also takes into account the missing levels. On the basis of our data sets we demonstrate that the power spectrum of level fluctuations in combination with short- and long-range spectral fluctuations provides a powerful tool for the determination of the fraction of randomly missing levels in systems that display wave chaos such as the three-dimensional chaotic microwave cavities. The experimental …
We derive the joint distribution of the moments $\mathrm{Tr}\, Q^κ$ ($κ\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be asymptotically Gaussian, and we compute explicitly averages and covariances. The results are in a compact form and have been verified numerically. The general methodology of proof and computations has a wide range of applications.
We consider the $1/N$-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting $N$ scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices $β=1$ and $β=2$) we obtain a recursion relation, which efficiently generates the coefficients of the $1/N$-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index $β$), we further show that reflection eigenvalues form a determinantal ensemble at $β=2$ and a new type of a Pfaffian ensemble at $β=4$. As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally ent…
Statistics of thermal to shot noise crossover in chaotic cavities
最近制定的量子传输的可积理论[Osipov和Kanzieper，Phys. Rev. Lett. 101，176804（2008）; arXiv：0806.2784]扩展到描述具有破缺时间反转对称性的混沌腔中噪声功率的样本到样本波动。集中在普遍的运输制度，我们确定的噪声功率累积量对温度的依赖性，施加的偏置电压，和在引线中的传播模式的数量。揭示并简要讨论了热散粒噪声散粒噪声交叉统计与朗道电导统计之间的内在联系。
We employ the Random Matrix Theory framework to calculate the density of zeroes of an $M$-channel scattering matrix describing a chaotic cavity with a single localized absorber embedded in it. Our approach extends beyond the weak-coupling limit of the cavity with the channels and applies for any absorption strength. Importantly it provides an insight for the optimal amount of loss needed to realize a chaotic coherent perfect absorbing (CPA) trap. Our predictions are tested against simulations for two types of traps: a complex network of resonators and quantum graphs.
We perform a study based on a random-matrix theory simulation for a three-terminal device, consisting of chaotic cavities on each terminal. We analyze the voltage drop along one wire with two chaotic mesoscopic cavities, connected by a perfect conductor, or waveguide, with one open mode. This is done by means of a probe, which also consists of a chaotic cavity that measure the voltage in different configurations. Our results show significant differences with respect to the disordered case, previously considered in the literature.
