Related papers: Large deviations at level 2.5 for Markovian open q…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). To this end, we first prove a stochastic…
We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…
Stochastic unravelings provide a useful way to represent open quantum system dynamics in terms of pure state realizations, and have been widely studied both from a fundamental and from a computational point of view. They were initially…
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the…
Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of…
To achieve efficient and reliable control of microscopic systems one should look for driving protocols that mitigate both the average dissipation and stochastic fluctuations in work. This is especially important in fast driving regimes in…
Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and…
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite…