Related papers: Markov constant and quantum instabilities
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
Adopting a statistical approach we study the degradation of entanglement of a quantum system under the action of an ensemble of randomly distributed Markovian noise. This enables us to address scenarios where only limited information is…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…
In this paper we develop the continuous averaging method of Treschev to work on the simultaneous Diophantine approximation and apply the result to give a new proof of the Nekhoroshev theorem. We obtain a sharp normal form theorem and an…
We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
This paper extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…
The traditional "explanation" for the observed acceleration of the universe is the existence of a positive cosmological constant. However, this can hardly be a truly convincing explanation, as an expanding universe is not expected to have a…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in…
We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an…
We extend the parametric geometry of numbers (initiated by Schmidt and Summerer, and deepened by Roy) to Diophantine approximation for systems of $m$ linear forms in $n$ variables, and establish a new connection to the metric theory via a…
We shortly review the progress in the domain of deterministic chaos for quantum dynamical systems. With the appropriately extended definition of quantum Lyapunov exponent we analyze various quantum dynamical maps. It is argued that, within…
In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to…
Two different dynamic models for belief change during evidence monitoring were evaluated: Markov and quantum. They were empirically tested with an experiment in which participants monitored evidence for an initial period of time, made a…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…