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Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
We analyse the correlated back and forth dynamics and dynamic heterogeneities, i.e. the presence of fast and slow ions, for a lithium metasilicate system via computer simulations. For this purpose we define, in analogy to previous work in…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting…
Non-equilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early time pre-equilibrium stage of high-energy heavy ion collisions. Besides their practical relevance they also…
We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological…
We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we…
We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave-function correlated and…
We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a…
Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic…
Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The…
The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…
The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers.…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…