Taming quantum noise for efficient low temperature simulations of open quantum systems
The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path
integral, is one of the most powerful numerical methods to simulate the dynamics of open …
integral, is one of the most powerful numerical methods to simulate the dynamics of open …
Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions.
Since analytic continuation is fundamentally an ill-posed problem, the causal space …
Since analytic continuation is fundamentally an ill-posed problem, the causal space …
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
Rational approximations of functions with singularities can converge at a root-exponential
rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax …
rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax …
Numerical conformal map** with rational functions
LN Trefethen - Computational Methods and Function Theory, 2020 - Springer
New algorithms are presented for numerical conformal map** based on rational
approximations and the solution of Dirichlet problems by least-squares fitting on the …
approximations and the solution of Dirichlet problems by least-squares fitting on the …
AAA rational approximation on a continuum
AAA rational approximation has normally been carried out on a discrete set, typically
hundreds or thousands of points in a real interval or complex domain. Here we introduce a …
hundreds or thousands of points in a real interval or complex domain. Here we introduce a …
AAA-least squares rational approximation and solution of Laplace problems
S Costa, LN Trefethen - Proceedings 8ECM, to appear, 2023 - content.ems.press
A two-step method for solving planar Laplace problems via rational approximation is
introduced. First, complex rational approximations to the boundary data are determined by …
introduced. First, complex rational approximations to the boundary data are determined by …
[PDF][PDF] The first five years of the AAA algorithm
The AAA algorithm, introduced in 2018, computes best or near-best rational approximations
to functions or data on subsets of the real line or the complex plane. It is much faster and …
to functions or data on subsets of the real line or the complex plane. It is much faster and …
Stochastic pole expansion method for analytic continuation of the Green's function
L Huang, S Liang - Physical Review B, 2023 - APS
In this paper, we propose an analytic continuation method to extract real-frequency spectral
functions from imaginary-frequency Green's functions of quantum many-body systems. This …
functions from imaginary-frequency Green's functions of quantum many-body systems. This …
The p-AAA algorithm for data-driven modeling of parametric dynamical systems
The AAA algorithm has become a popular tool for data-driven rational approximation of
single-variable functions, such as transfer functions of a linear dynamical system. In the …
single-variable functions, such as transfer functions of a linear dynamical system. In the …
Estimating experimental dispersion curves from steady-state frequency response measurements
Dispersion curves characterize the frequency dependence of the phase and the group
velocities of propagating elastic waves. Many analytical and numerical techniques produce …
velocities of propagating elastic waves. Many analytical and numerical techniques produce …