Related papers: State space decomposition for nonautonomous dynami…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We…
We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known…
This paper introduces a PDE-free algorithmic framework for the local decomposition of classical forces in arbitrary dimensions. By representing a force field as a differential $1$-form (work form), we employ the homotopy operator on a…
We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the…
In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…
What determines whether an organism or collective will survive under particular conditions? This question is asked across the life sciences when determining adaptive fit, developing efficacious treatments for diseases, and assessing the…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems.…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Coherent states with large amplitudes are traditionally thought of as the best quantum mechanical approximation of classical behavior. Here we argue that, far from being classical, coherent state are in fact highly entangled. We demonstrate…
The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…
We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce…
We consider the dynamics of quantum systems which possess stationary states as well as slowly decaying, metastable states arising from the perturbation of bound states. We give a decomposition of the propagator into a sum of a stationary…
The general aim of this paper is to supply a method to decide whether a discrete system decoheres or not, and under what conditions decoherence occurs, with no need of appealing to computer simulations to obtain the time evolution of the…
We provide a result on the coherent states decomposition for functions in $L^2 (\Bbb T^n)$ where $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$. Suddenly, we study such a decomposition with respect to the quantum dynamics related to semiclassical…
We will show how it is possible to generate entangled states out of unentangled ones on a bipartite system by means of dynamical boundary conditions. The auxiliary system is defined by a symmetric but not self-adjoint Hamiltonian and the…
A linear decomposition of states underpins many classical systems. This is the case of the Helmholtz decomposition, used to split vector fields into divergence-free and potential components, and of the dry Boussinesq system in atmospheric…