Related papers: Improved performance in quantum transport calculat…
In this paper, we propose a method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in…
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kind of fundamental structures are given,…
Landauer-B\"uttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations.…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
In this study, we propose a recursive approach to study the transport properties of atomic wires. It is based upon a real-space block-recursion technique with Landauer's formula being used to express the conductance as a scattering problem.…
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 devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral…
We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient…
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
An easy to implement and powerful method for the solution of 3D scattering problems that can be well described by Helmholtz equation is presented. The matrix algebra used provides excellent stability versus the number of junctions as well…
We present a self-contained description of the wave-function matching (WFM) method to calculate electronic quantum transport properties of nanostructures using the Landauer-B\"uttiker approach. The method is based on a partition of the…
Matrix mechanisms are often used to provide unbiased differentially private query answers when publishing statistics or creating synthetic data. Recent work has developed matrix mechanisms, such as ResidualPlanner and Weighted Fourier…
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of…
Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…
In one dimensional transport problems the scattering matrix $S$ is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For $S$ a random unitary matrix, the singular value probability…
Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3): A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
We discuss the electromagnetic scattering and radiation problems of multilayered spheres, reviewing the history of the Lorentz-Mie theory and the numerical stability issues encountered in handling multilayered spheres. By combining…