相关论文: On exact summations in long-range interactions
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion…
The recently proposed effective potential theory [Phys. Rev. Lett. 110, 235001 (2013)] allows evaluating transport in coupled plasmas with the well-developed formalisms for systems with binary collisions. To facilitate practical…
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…
Long-range interactions are essential determinants of chemical system behaviour across diverse environments. We present a foundation framework that integrates explicit polarizable long-range physics with an equivariant graph neural network…
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we…
Mediation analysis is concerned with the decomposition of the total effect of an exposure on an outcome into the indirect effect through a given mediator, and the remaining direct effect. This is ideally done using longitudinal measurements…
This paper studies convergence to equilibrium for second-order Langevin dynamics under general growth conditions on the potential. Although we are principally motivated by the case when the potential is singular, e.g. when the dynamics has…
By assuming some widely-believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop…
A method for extending traditional plasma transport theories into the strong coupling regime is presented. Like traditional theories, this is based on a binary scattering approximation, but where physics associated with many body…
The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics. Any simulation based on a fluid model inherently requires a closure relation for the high order plasma…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We investigate the ground state properties of a family of $N$-body systems in 1-dimension, trapped in a polynomial potential and having long range 2-body interaction in addition to the inverse square potential studied in the…
We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
The scattering of two and more particles at low energies is described by the so called effective-range expansion. The leading terms of this expansion are the scattering length and effective range. The analytic expressions for both of the…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…