Related papers: Higher-Order Structure of Hamiltonian Truncation E…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input…
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…
We consider the large order behavior of the perturbative expansion of the scalar $\varphi^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…
We consider conformal perturbation theory for $n$-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size $\epsilon$ around the…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…
We present the complete next-to-leading order short-distance QCD corrections to the effective \dstwo -hamiltonian in the Standard Model. The calculation of the coefficient $\eta_3$ is described in great detail. It involves the two-loop…
It may be possible to derive a constituent approximation for bound states in QCD using hamiltonian light-front field theory. Cutoffs that violate explicit gauge invariance and Lorentz covariance must be employed. A similarity…
Experiments at the LHC are collecting a wealth of data with an unprecedented level of precision. As a consequence, the theoretical error is now starting to lag behind the experimental one, and a ceaseless effort is required to reduce the…
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…
We present the two-loop corrected operator matrix elements contributing to the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$ calculated up to finite terms which survive in the limit $\epsilon = N - 4 \to 0$. These…
This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…
We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…