Related papers: Chebyshev-BdG: an efficient numerical approach to …
Calculation of current and order parameter distribution in inhomogeneous superconductors is often based on a self-consistent solution of Eilenberger equations for quasiclassical Green's functions. Compared to the original Gorkov equations,…
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…
Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
We present and review an efficient method to calculate the retarded Green's function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. The…
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a…
Self-consistent approaches to superfluid many-fermion systems in 3-dimensions (and subsequent time-dependent approaches) require a large number of diagonalizations of very large dimension hermitian matrices, which results in enormous…
Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function…
Recent experiments on mesoscopic normal-metal--superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energy $k_B T \le E_{Th}$. We describe the properties…
Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially…
We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…
The boundary Green's function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We present a new method to determine the best constant of the Sobolev-type embedding in one dimension with a norm including a bounded inhomogeneous potential term. This problem is closely connected to the Green function of the Schr\"odinger…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
Path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of large bosonic systems in a recent work (Hirshberg et al., PNAS, 116, 21445 (2019)). In this work we extend PIMD techniques to study Green's…
We demonstrate an efficient nonequilibrium Green's function transport calculation procedure based on the real-space finite-difference method. The direct inversion of matrices for obtaining the self-energy terms of electrodes is…