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Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…
In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of `synthetic dimensions' has recently emerged as a powerful way to emulate…
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
We characterize the singularity set of massless theories by giving a complete set of the Landau polynomials. We find the general form of Gauss-Manin connection. We show that for massless theories the dependence on momenta decouples from the…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system.…
We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine,…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
We consider a non-minimal coupling of a perfect fluid matter system with geometry, which the coupling function is taken to be an arbitrary function of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved…
Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial…
We explore the dynamics of cosmological models with two coupled dark components with energy densities $\rho_A$ and $\rho_B$. We assume that the coupling is of the form $Q=Hq(\rho_A,\rho_B)$, so that the dynamics of the two components turns…
Recent developments dedicated to the building of multiscale mechanical and chemical constitutive laws for energetic molecular crystals are presented and discussed. In particular, various tools have been specifically incorporated in…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or `dust', this approach gives the correct results for scales much smaller than the cosmological horizon,…
We show that the strong CP problem can, in principle, be solved dynamically by adding extra-dimensions with compact topology. To this aim we consider a toy model for QCD, which contains a vacuum angle and a strong CP like problem. We…