arXiv subjects

Hector Mera

Publications and source records attributed to Hector Mera.

5 recordsLinked to original sources

arXiv2018

Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants

We demonstrate that a Meijer-G-function-based resummation approach can be successfully applied to approximate the Borel sum of divergent series, and thus to approximate the Borel-Écalle summation of resurgent transseries in quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parameterized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-Hypergeometric method [Mera {\it et al.} Phys. Rev. Lett. {\bf 115}, 143001 (2015)]. Here we illustrate the ability of this technique in various examples from QFT, traditionally employed as benchmark models for resummation, such as: 0-dimensional $ϕ^4$ theory, $ϕ^4$ with degenerate minima, self-interacting QFT in 0-dimensions, and the computation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

hep-th↗

arXiv2015

Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium

A newly developed hypergeometric resummation technique [H. Mera et al., Phys. Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain conserving approximations within the self-consistent nonequilibrium many-body perturbation theory. We demonstrate the usefulness of this technique by calculating the phonon-limited electronic current in a model of a single-molecule junction within the self-consistent Born approximation for the electron-phonon interacting system, where the perturbation expansion for the nonequilibrium Green function in powers of the free bosonic propagator typically consists of a series of non-crossing \sunset" diagrams. Hypergeometric resummation preserves conservation laws and it is shown to provide substantial convergence acceleration relative to more standard approaches to self-consistency. This result strongly suggests that the convergence of the self-consistent \sunset" series is limited by a branch-cut singularity, which is accurately described by Gauss hypergeometric functions. Our results showcase an alternative approach to conservation laws and self-consistency where expectation values obtained from conserving perturbation expansions are \summed" to their self-consistent value by analytic continuation functions able to mimic the convergence-limiting singularity structure.

cond-mat.mes-hall↗

arXiv2014

Nonperturbative Quantum Physics from Low-Order Perturbation Theory

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built in analytic structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel-consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

cond-mat.stat-mech↗

arXiv2010

Charged impurity scattering and mobility in gated silicon nanowires

We study the effects of charged impurity scattering on the electronic transport properties of <110>-oriented Si nanowires in a gate-all-around geometry, where the impurity potential is screened by the gate, gate oxide and conduction band electrons. The electronic structure of the doped nanowires is calculated with a tight-binding method and the transport properties with a Landauer-Buttiker Green functions approach and the linearized Boltzmann transport equation (LBTE) in the first Born approximation. Based on our numerical results we argue that: (1) There are large differences between Phosphorous (P) and Boron (B) doped systems, acceptors behaving as tunnel barriers for the electrons, while donors give rise to Fano resonances in the transmission. (2) As a consequence, the mobility is much larger in P- than in B-doped nanowires at low carrier density, but can be larger in B-doped nanowires at high carrier density. (3) The resistance of a single impurity is strongly dependent on its radial position in the nanowire, especially for acceptors. (4) As a result of subband structure and screening effects, the impurity-limited mobility can be larger in thin nanowires embedded in HfO2 than in bulk Si. Acceptors might, however, strongly hinder the flow of electrons in thin nanowires embedded in SiO2. (5) The perturbative LBTE largely fails to predict the correct mobilities in quantum-confined nanowires.

cond-mat.mes-hall↗

arXiv2008

Continuous corrections to the molecular Kohn-Sham gap and virtual orbitals

We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that the resulting mean-field scheme yields, in finite systems, virtual orbitals and energy gaps in better agreement with those predicted by quasiparticle theory. The proposed correction term is a scissors-like operator of the form $(\hat{I}-\hatρ)δ\hat{H}(\hat{I}-\hatρ)$, where $\hat{I}$ is the identity operator, $\hatρ$ the density matrix of the N-particle system and $δ\hat{H}$ is either the difference between the N+1- and N-particle Kohn-Sham Hamiltonians or a non-self-consistent approximation to it. Such a term replaces the Kohn-Sham virtual orbitals of the $N$-particle system by the HOMO and virtual orbitals of the system with $N+1$ particles in an attempt to mimic a true quasiparticle spectrum. Using a local density approximation (LDA) we compute the gaps of a variety of small molecules finding good agreement with experiment and computationally more demanding methods. For these systems we examine the physical origin of this gap correction and show that so-called band gap discontinuity, $Δ_{xc}$, contains electrostatic contributions that do not originate from the discontinuity in the exchange-correlation potential. The similarity between the corrected and Hartree-Fock virtual orbitals is illustrated and the extent to which the bare LDA virtual orbitals are improved is considered. The lack of band-gap discontinuity and the presence of self-interaction errors in the proposed correction are also discussed.

cond-mat.other↗