Related papers: (Non)local $\Gamma$-convergence
This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new…
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range,…
Quantum mechanical nonlocality considered as posssible mechanism of long-distance correlations in living organisms and plants, which regulate their coherent development and functioning. It's shown that Doebner-Goldin nonlinear quantum…
We study the rate of convergence of some nonlocal functionals recently considered by Bourgain, Brezis and Mironescu. In particular we establish the $\Gamma$-convergence of the corresponding rate functionals, suitably rescaled, to a limit…
We establish some new results about the $\Gamma$-limit, with respect to the $L^1$-topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica Bending Energy for curves in the plane.
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
We revise the cosmological interaction between dark energy and dark matter. More precisely, we focus on models that support compartmentalization or co-existence in the dark sector of the universe. Within the framework of a homogeneous and…
In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of species. Our analysis relies on the observation that the graph…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we…
We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only…
We establish the equivalence between the continuum limit of the quantum spherical model with competing interactions, which is relevant to the investigation of Lifshitz points, and the O(N) nonlinear sigma model with the addition of higher…
We study the $\Gamma$-convergence of sequences of free discontinuity functionals with linear growth defined in the space ${\rm BD}$ of functions with bounded deformation. We prove a compactness result with respect to $\Gamma$-convergence…
We present the dynamical analysis for interacting quintessence, considering linear cosmological perturbations. Matter perturbations improve the background analysis and viable critical points describing the transition of the three…
We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
Many models of quintessence predict a time variation of the fundamental constants as well as a composition-dependent gravity like long-range force mediated by the cosmon. We present bounds for the cosmon coupling to matter and radiation…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…