相关论文: Vacuum stability and the Cholesky decomposition

We consider a possible application of the Wa\.zewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such…

We perform a detailed phase-space analysis of a class of k-essence cosmology. We find the critical points can be divided into three classes: points unstable but the model stable, both points and the model stable, points stable but the model…

The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick…

In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor…

We study scaling symmetry in a class of non-minimally coupled scalar field in a background of Friedmann-Robertson-Walker (FRW) spacetime. We use a non-minimally coupling $R L^{(\varphi)}$. We find the corresponding conserved charge of that…

We consider stability theory for Polish spaces and more generally for definable structures (say, with elements of a set of reals). We clarify by proving some equivalent conditions for $\aleph_0$-stability. We succeed to prove existence of…

Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…

In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient…

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and…

We are interested in the long-time behaviour of the kinetic Vicsek equation, rigorously derived as the mean-field limit~\cite{bolley2012meanfield} of a coupled system of~$N$ stochastic differential equations describing particles moving at…

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast…

Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…

Under the assumption that the cosmological constant vanishes in the true ground state with lowest possible energy density, we argue that the observed small but finite vacuum-like energy density can be explained if we consider a theory with…

We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of…

The singularity of the black hole solutions obtained before in M{\o}ller's theory are studied. It is found that although the two solutions reproduce the same associated metric the asymptotic behavior of the scalars of torsion tensor and…

This article studies a class of semilinear scalar field equations on the real line with variable coefficients in the linear terms. These coefficients are not necessarily small perturbations of a constant. We prove that under suitable…

We study vacuum stability in 1+1 dimensional Conformal Field Theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective…

We will present the way to derive a de Sitter inflationary solution within the so-called Starobinsky-Bel-Robinson gravity. Then, we will show by using the dynamical system method whether the obtained solution is stable or not. According to…

Building on a quasi-chemical formulation of solution theory, this paper proposes a self consistent molecular field theory for packing problems in classical liquids, and tests the theoretical predictions for the excess chemical potential of…

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the Thomas-Fermi approach. The Thomas-Fermi solutions statisfy the stability condition against scaling. We apply the…