Related papers: Universal and nonuniversal probability laws in Mar…
We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the…
We consider a one-dimensional random walk (RW) with a continuous and symmetric jump distribution, $f(\eta)$, characterized by a L\'evy index $\mu \in (0,2]$, which includes standard random walks ($\mu=2$) and L\'evy flights ($0<\mu<2$). We…
We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied…
For classical Markovian stochastic systems, past and future events become statistically independent when conditioned to a given state at the present time. Memory non-Markovian effects break this condition, inducing a non-vanishing…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
A sudden change of the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges…
We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be…
The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
In the present paper, we consider a class of Markov processes on the discrete circle which has been introduced by K\"onig, O'Connell and Roch. These processes describe movements of exchangeable interacting particles and are discrete…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…
The non-Markovian nature of open quantum dynamics lies in the structure of the multitime correlations, which are accessible by means of interventions. Here, by examining multitime correlations, we show that it is possible to engineer…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y,…
We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…
We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the…