Related papers: Quantum conductance problems and the Jacobi ensemb…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
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…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
We present a general method for calculating coherent electronic transport in quantum wires and tunnel junctions. It is based upon a real space high order finite difference representation of the single particle Hamiltonian and wave…
We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of…
In this paper, we provide a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In this method, the columns of the quaternion matrix are orthogonalized in pairs by using…
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the…
We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is…
The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables…
We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
Examples of the $\beta$-Jacobi ensemble specify the joint distribution of the transmission eigenvalues in scattering problems. In this context, there has been interest in the distribution of the trace, as the trace corresponds to the…
For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such…