Related papers: Spectral delineation of Markov Generators: Classic…

We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2…

Qualitative features of the Manakov top are discussed for the classical and quantum versions of the problem. Energy-momentum diagram for this integrable classical problem and quantum joint spectrum of two commuting observables for…

In this paper, we study Markov dynamics on unitary duals of compact quantum groups. We construct such dynamics from characters of quantum groups. Then we show that the dynamics have generators, and we give an explicit formula of the…

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum…

We investigate the fundamental expressivity limits of quantum reservoir computing (QRC) by establishing a formal connection to parametrized quantum circuit quantum machine learning (PQC-QML). We analytically prove, and numerically…

Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…

We prove that continuous spectrum- and commutativity-preserving maps to $\mathcal{M}_n(\mathbb{C})$ from the space of normal (real or complex) $n\times n$, $n\ge 3$ matrices with spectra contained in a given continuous-injection interval…

Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…

We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…

We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…

We consider a general multivariate affine stochastic recursion and the associated Markov chain on $\mathbb R^{d}$. We assume a natural geometric condition which implies existence of an unbounded stationary solution and we show that the…

The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of…

We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms…

Theories with Planck-scale deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the non-trivial structure of momentum space of these models is reflected in a…

Perturbative quantum corrections to primordial power spectra are important for testing the robustness and the regime of validity of inflation as an effective field theory. Although this has been done extensively for the density power…

Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…

We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial…

Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$…

Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…

In this paper, we consider continuous-time Markov chains with a finite state space under nonlinear expectations. We define so-called Q-operators as an extension of Q-matrices or rate matrices to a nonlinear setup, where the nonlinearity is…