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While the Landauer viewpoint constitutes a modern basis to understand nanoscale electronic transport and to realize first-principles implementations of the non-equilibrium Green's function (NEGF) formalism, seeking an alternative picture…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is…
Noncollinear (NC) magnetism and spin-orbit coupling (SOC) are indispensable for predictive ab initio materials simulations with pronounced relativistic effects and magnetic frustration, yet they significantly increase the cost of…
Due to their unique electrical properties, graphene nanoribbons (GNRs) show great promise as the building blocks of novel electronic devices. However, these properties are strongly dependent on the geometry of the edges of the graphene…
Gradient Descent (GD) and its variants are the primary tool for enabling efficient training of recurrent dynamical systems such as Recurrent Neural Networks (RNNs), Neural ODEs and Gated Recurrent units (GRUs). The dynamics that are formed…
Since the initial development of one-dimensional electron gases (1DEG) two decades ago, there has been intense interest in both the fundamental physics and the potential applications, including quantum computation, of these quantum…
The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter…
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…
An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system…
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…
We derive a closed equation of motion for the one particle density matrix of a quantum system coupled to multiple baths using the Redfield master equation combined with a mean-field approximation. The steady-state solution may be found…
The performance potential for simulating quantum electron transport on graphical processing units (GPUs) is studied. Using graphene ribbons of realistic sizes as an example it is shown that GPUs provide significant speed-ups in comparison…
We consider formulations of the functional renormaliztion-group flow for correlated electronic systems, having the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those…
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…
With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational methods are required to take advantage of such extreme-scale machines. In this…
In this thesis we showed that Non-equilibrium Green's Function Perturbation Theory (NEGF) is really the overarching perturbative transport theory. This is shown in great detail by using NEGF as a starting point and developing in 3…
We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum…
We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the…