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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…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem. Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We consider a…
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…
We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…
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…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
We consider a small interacting sample coupled to several non-interacting leads. Initially, the system is at thermal equilibrium. At some instant $t_0$ the system is set into the so called partition-free transport scenario by turning on a…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of Tchetgen Tchetgen et. al. (2021), which allows (i) interaction…
Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains.…
We derive a method to efficiently compute the Green function of on arbitrary Hamiltonians defined on semi-infinite and periodic quasi-one-dimensional lattices. Computing the Green function is the backbone of quantum transport, electronic…
For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful to derive several general…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…