The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under assumption of broken time-reversal symmetry, this result is further utilised to (i) calculate the density and correlation functions of reflection eigenvalues, and (ii) analyse fluctuations properties of the Landauer conductance for the illustrative example of asymmetric chaotic cavity. Further extensions of the theory are pinpointed.
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 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 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.
The Painlevé transcendents discovered at the turn of the XX century by pure mathematical reasoning, have later made their surprising appearance -- much in the way of Wigner's "miracle of appropriateness" -- in various problems of theoretical physics. The notable examples include the two-dimensional Ising model, one-dimensional impenetrable Bose gas, corner and polynuclear growth models, one dimensional directed polymers, string theory, two dimensional quantum gravity, and spectral distributions of random matrices. In the present contribution, ideas of integrability are utilized to advocate eme…
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.
Within the random matrix theory approach to quantum scattering, we derive the distribution of the Wigner-Smith time delay matrix $\mathcal{Q}$ for a chaotic cavity with uniform absorption, coupled via $N$ perfect channels. In the unitary class $β=2$ we obtain a compact expression for the distribution of the full matrix in terms of a matrix integral. In the other symmetry classes we derive the joint distribution of the eigenvalues. We show how the large $N$ properties of this distribution can be analysed in terms of two interacting Coulomb gases living on two different supports. As an applicati…
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 bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are present and the number of open channels, $M$, is small. In contrast to previous approaches, ours is non-perturbative in $M$; instead, we arrive at an explicit expression in the form of a power series in the barrier's reflectivity, whose coefficients are rational functions of $M$. For general moments we must require that the barriers are equal and time reversal sy…
Conventional microlasing of electromagnetic waves requires (1) a high $Q$ cavity and (2) a mechanism for directional emission. Previous theoretical and experimental work demonstrated that the two requirements can be met with deformed dielectric cavities that generate chaotic ray dynamics. Is it possible for a massless Dirac spinor wave in graphene or its photonic counterpart to exhibit a similar behavior? Intuitively, because of the absence of backscattering of associated massless spin-1/2 particles and Klein tunneling, confining the wave in a cavity for a long time seems not feasible. Deformi…
