Related papers: Constructing equilibrium states for Smale spaces
This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
We introduce sparse versions of function spaces that are relevant to characterize the solutions of Euler equations without concentration. The standard Sobolev space $H^{-1}$ is given a sparse structure that allows to measure the degree of…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…
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…
We show that, for a robust ($C^2$-open) class of random non-uniformly expanding maps, there exists equilibrium states for a large class of potentials.In particular, these sytems have measures of maximal entropy. These results also give a…
This work investigates the topical problem of balancing the shallow water equations over the bottom steps of different heights. The current approaches in the literature are essentially based on mathematical analysis of the hyperbolic system…
We unify two recent results concerning equilibration in quantum theory. We first generalise a proof of Reimann [PRL 101,190403 (2008)], that the expectation value of 'realistic' quantum observables will equilibrate under very general…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
A standard result by Smale states that n dimensional strongly cooperative dynamical systems can have arbitrary dynamics when restricted to unordered invariant hyperspaces. In this paper this result is extended to the case when all solutions…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
For problems relating to fracture, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical system should yield the same structure and elastic properties as the QM domain for states near…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
In this paper we study the well-posedness of weakly hyperbolic systems with time dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are H\"older with respect to $t$. In the past these kind of…
We investigate some properties of the dynamical system of point vortices on the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint equivariant momentum map J. The relative equilibrium conditions are found and the…
The structure of the state-vector space for the two-mode parabose system is investigated and a complete set of state-vectors is constructed. The basis vectors are orthonormal in order $p=2$. In order $p=2$, conserved-charge parabose…
We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…