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Many-body descriptors are widely used to represent atomic environments in the construction of machine learned interatomic potentials and more broadly for fitting, classification and embedding tasks on atomic structures. It was generally…
We compute the strengths of zero-th order (in eccentricity) three-body resonances for a co-planar and low eccentricity multiple planet system. In a numerical integration we illustrate that slowly moving Laplace angles are matched by…
We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target…
A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…
In this paper we first compute the out-of-time-order correlators (OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized…
Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that…
Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of…
In this study, we have found a new random ordered phase in isotropic models with many-body interactions. Spin correlations between neighboring planes are rigorously shown to form a long-range order, namely coplanar order, using a unitary…
Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…
Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On…
The lowest-lying states of the Borromean nucleus $^{17}$Ne ($^{15}$O+$p$ + $p$) and its mirror nucleus $^{17}$N ($^{15}$N+$n$ + $n$) are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem becomes non-perturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs…
Relativistic secular perturbation theory has ignited significant interest in uncovering intricate cross-term effects, especially the interplay between 1PN and quadrupole terms. While most existing studies rely on the Lagrangian planetary…
We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
We present theoretical ground state energies and their uncertainties for p-shell nuclei obtained from chiral effective field theory internucleon interactions as a function of chiral order, fitted to two- and three-body data only. We apply a…
A normal form theory for non--quasi--periodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in [15] to prove, in the averaged, planar three--body problem, the existence of a plenty…
Different approaches have been applied to the calculation of form factors of various hadronic systems within relativistic quantum mechanics. In a one-body current approximation, they can lead to results evidencing large discrepancies.…
Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…