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It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a…

Quantum Physics · Physics 2025-05-02 Gabriele Pinna , Oliver Lunt , Curt von Keyserlingk

In this article we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the…

Strongly Correlated Electrons · Physics 2017-01-04 Johan Schött , Erik G. C. P. van Loon , Inka L. M. Locht , Mikhail Katsnelson , Igor Di Marco

This work reports a theoretical framework that combines the auxiliary coherent potential approximation (ACPA-DMFT) with dynamical mean-field theory to study strongly correlated and disordered electronic systems with both diagonal and…

Strongly Correlated Electrons · Physics 2025-02-12 Zelei Zhang , Jiawei Yan , Li Huang , Youqi Ke

The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…

Mesoscale and Nanoscale Physics · Physics 2026-04-15 Robert Meiners Fuchs , Juanjuan Ren , Stephen Hughes , Marten Richter

Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…

Numerical Analysis · Mathematics 2026-01-09 Shengyan Li , Qi Sun , Xuejun Xu , Bowen Zheng

In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 G. Metalidis , P. Bruno

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…

Strongly Correlated Electrons · Physics 2017-06-30 Anders W. Sandvik

Approximations based on rational functions are widely used in various applications across computational science and engineering. For univariate functions, the adaptive Antoulas-Anderson algorithm (AAA), which uses the barycentric form of a…

Numerical Analysis · Mathematics 2025-02-06 Linus Balicki , Serkan Gugercin

We derive equations of motion for Green's functions of the multi-orbital Anderson impurity model by differentiating symmetrically with respect to all time arguments. The resulting equations relate the one- and two-particle Green's function…

Strongly Correlated Electrons · Physics 2019-08-14 Josef Kaufmann , Patrik Gunacker , Alexander Kowalski , Giorgio Sangiovanni , Karsten Held

Quantum Monte Carlo (QMC) methods are uniquely capable of providing exact simulations of quantum many-body systems. Unfortunately, the applications of a QMC simulation are limited because extracting dynamic properties requires solving the…

Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…

Numerical Analysis · Mathematics 2025-09-16 Qi Sun , Shengyan Li , Bowen Zheng , Lili Ju , Xuejun Xu

A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…

Numerical Analysis · Mathematics 2021-07-27 E. Stella , C. L. Ladera , G. Donoso

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…

Mesoscale and Nanoscale Physics · Physics 2016-10-14 Mariana M. Odashima , Beatriz G. Prado , E. Vernek

In linear perturbation theory, all information about the growth of structure is contained in the Green's function, or equivalently, transfer function. These functions are generally computed using numerical codes or by phenomenological…

Cosmology and Nongalactic Astrophysics · Physics 2016-01-27 Zachary Slepian , Daniel J. Eisenstein

Measuring the vibronic spectrum probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body…

Chemical Physics · Physics 2018-12-05 Sven Karsten , Sergei D. Ivanov , Sergey I. Bokarev , Oliver Kühn

Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the…

Strongly Correlated Electrons · Physics 2024-11-28 Zhe Zhao , Jingping Xu , Ce Wang , Yaping Yang

We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic external excitation. The kernel of this integral equation is a…

Dynamical Systems · Mathematics 2019-05-10 Shobhit Jain , Thomas Breunung , George Haller

We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test…

Condensed Matter · Physics 2009-10-28 J. Bonca , J. E. Gubernatis

We introduce the projected Green's function technique to study quasi-periodic systems such as the Andre-Aubry-Harper (AAH) model and beyond. In particular, we use projected Green's functions to construct a "rational approximate" sequence of…

Mesoscale and Nanoscale Physics · Physics 2022-08-11 Dan S. Borgnia , Ashvin Vishwanath , Robert-Jan Slager

A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…

Chemical Physics · Physics 2019-09-17 Prashant Rai , Khachik Sargsyan , Habib Najm , So Hirata