Related papers: Ergodic and Mixing Quantum Channels in Finite Dime…
It is known that the Dobrushin's ergodicity coefficient is one of the effective tools to study a behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on…
We study the limiting behavior of a random dynamic system driven by a stochastic chain. Our main interest is in the chains that are not necessarily ergodic but rather decomposable into ergodic classes. To investigate the conditions under…
We address asymptotic decoupling in the context of Markovian quantum dynamics. Asymptotic decoupling is an asymptotic property on a bipartite quantum system, and asserts that the correlation between two quantum systems is broken after a…
Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external…
We investigate the effect of ergodic inclusions in putative many-body localized systems. To this end, we consider the random field Heisenberg chain, which is many-body localized at strong disorder and we couple it to an ergodic bubble,…
Quantum embedding methods have become a powerful tool to overcome deficiencies of traditional quantum modelling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to…
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…
We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site…
We demonstrate an innovative quantum Hall circuit with variable geometry employing the moveable electrostatic potential induced by a biased atomic force microscope tip. We exploit this additional degree of freedom to identify the…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
We propose a version of the Quantum Ergodicity theorem on large regular graphs of fixed valency. This is a property of delocalization of "most" eigenfunctions. We consider expander graphs with few short cycles (for instance random large…
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…
Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this…
We study the ergodic and non-ergodic behaviors of a clean Jaynes-Cummings-Hubbard chain for different parameters based on the average level spacings and the generalized fractal dimensions of eigenstates by using exact diagonalization. It…
We study distribution of orbits sampled at polynomial times for uniquely ergodic topological dynamical systems $(X, T)$. First, we prove that if there exists an increasing sequence $(q_n)$ for which the rigidity condition \[…
Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal…
Quantum channels can describe all transformations allowed by quantum mechanics. We provide an explicit universal protocol to construct all possible quantum channels, using a single qubit ancilla with quantum non-demolition readout and…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and…
The particle Gibbs (PG) sampler is a systematic way of using a particle filter within Markov chain Monte Carlo (MCMC). This results in an off-the-shelf Markov kernel on the space of state trajectories, which can be used to simulate from the…