Related papers: A hyperbolic slicing condition adapted to Killing …
We theoretically investigate the effect of multi-mode dynamics on the creation of macroscopic superposition states (spin-cat states) in Bose-Einstein condensates via one-axis twisting. A two-component Bose-Einstein condensate naturally…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…
A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions…
We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
In a static spacetime, the Killing time can be used to measure the time required for signals or objects to propagate between two of its orbits. By further restricting to spherically symmetric cases, one obtains a natural association between…
In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS…
In the hyperbolic slicing of de Sitter space appropriate for open universe models, a curvature scale is present and supercurvature fluctuations are possible. In some cases, the expansion of a scalar field in the Bunch-Davies vacuum includes…
Consider a holomorphic automorphism acting hyperbolically on an invariant compact set. It has been conjectured that the arising stable manifolds are all biholomorphic to Euclidean space. Such a stable manifold is always equivalent to the…
We investigate observational constraints on the Brans-Dicke cosmological model using observational data coming from distant supernovae type Ia, the Hubble function $H(z)$ measurements, information coming from the Alcock-Paczy{\'n}ski test,…
Standard numerical methods for hyperbolic PDEs require for stability a CFL-condition which implies that the time step size depends on the size of the elements of the mesh. On cut-cell meshes, elements can become arbitrarily small and thus…
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for…
The investigation of the nonequilibrium quantum dynamics of bosonic many-body systems is very challenging due to the excessively growing Hilbert space and poses a major problem for their theoretical description and simulation. We present a…
The paper studies the long time behavior of a system that describes the motion of a piece of elastic membrane driven by surface tension and inner air pressure. The system is a degenerate quasilinear hyperbolic one that involves the mean…
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important research achievements, a conceptually simple approach is…
The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space dimension, subject to either Neumann or Dirichlet boundary conditions. To perform…
Two first order strongly hyperbolic formulations of scalar-tensor theories of gravity (STT) allowing nonminimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…