Related papers: Analytic influence functionals for numerical Feynm…
We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent…
We consider the numerical evaluation of a class of double integrals with respect to a pair of self-similar measures over a self-similar fractal set (the attractor of an iterated function system), with a weakly singular integrand of…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral…
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form $E\left[\exp(A_T)\right]$, the (effective) action…
Loop amplitudes for massless five particle scattering processes contain Feynman integrals depending on the external momentum invariants: pentagon functions. We perform a detailed study of the analyticity properties and cut structure of…
We study the dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude…
Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the region $|z|<1$ and satisfying \begin{align*} {\rm Re\,}…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
Wang and Tchetgen Tchetgen (2017) studied identification and estimation of the average treatment effect when some confounders are unmeasured. Under their identification condition, they showed that the semiparametric efficient influence…
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
There are many nonparametric objects of interest that are a function of a conditional distribution. One important example is an average treatment effect conditional on a subset of covariates. Many of these objects have a conditional…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
A method for reducing Feynman integrals, depending on several kinematic variables and masses, to a combination of integrals with fewer variables is proposed. The method is based on iterative application of functional equations proposed by…
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly…
Influence functions approximate the effect of training samples in test-time predictions and have a wide variety of applications in machine learning interpretability and uncertainty estimation. A commonly-used (first-order) influence…
The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
Numerical analytical heat transfer models play a critical role in geothermal design and feasibility studies. Classical solutions, such as those proposed by Gringarten et al. 1975, rely on simplified assumptions and systematically…