Related papers: A highly accurate procedure for computing globally…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
Within this paper we outline a method able to generate truly minimal basis sets which describe either a group of bands, a band, or even just the occupied part of a band accurately. These basis sets are the so-called NMTOs, Muffin Tin…
We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the…
In this work a framework for quantum transport simulation from first principles is introduced, focusing on the coherent case. The model is based on the non-equilibrium Green's function (NEGF) formalism and maximally localized Wannier…
We provide a constructive proof of exponentially localized Wannier functions and related Bloch frames in 1- and 2-dimensional time-reversal symmetric (TRS) topological insulators. The construction is formulated in terms of periodic TRS…
The nontrivial evolution of Wannier functions (WF) for the occupied bands is a good starting point to understand topological insulator. By modifying the definition of WFs from the eigenstates of the projected position operator to those of…
To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$.…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, $\mu$ and $\nu$, which is useful in many applications. Available algorithms for computing these maps do not appear to…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
We introduce the notion of Schr\"odinger integral operators and prove sharp local and global regularity results for these (including propagators for the quantum mechanical harmonic oscillator). Furthermore we introduce general classes of…
We present a technique for partitioning the total energy from a semi-local density functional theory calculation into contributions from individual electronic states in a localized Wannier basis. We use our technique to reveal the key role…
In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we…
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta…
We show that two elementary worldline path integrals-the thermal partition function of the harmonic oscillator and the one-loop effective action of scalar QED in a constant field strength-exhibit a natural form of supersymmetric…
In many applications that involve the inference of an unknown smooth function, the inference of its derivatives will often be just as important as that of the function itself. To make joint inferences of the function and its derivatives, a…