相关论文: Recent new methods and applications of the differe…

In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…

Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

We develop a method to obtain $\epsilon$-expansions of massless two-point integrals in position space, based on the constraints implied by symmetries of the asymptotic expansion of conformal four-point integrals. Together with parametric…

We show that the new relation between master integrals recently obtained in Ref. [1] can be reproduced using the integration-by-parts technique implemented with an effective mass. In fact, this relation is recovered as a special case of a…

We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…

The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…

The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct…

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…

For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in…

We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…

Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…

The computation of master integrals from their differential equations requires boundary values to be supplied by an independent method. These boundary values are often desired at singular kinematical points. We demonstrate how the auxiliary…

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…

We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equa- tions with canonical bases. We obtain results in terms of multiple…

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…