Related papers: On quantum Stochastic Master equations
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
We derive the quantum stochastic master equation for bosonic systems without measurement theory but control theory. It is shown that the quantum effect of the measurement can be represented as the correlation between dynamical and…
We present a master equation describing the interaction of light with dielectric objects of arbitrary sizes and shapes. The quantum motion of the object, the quantum nature of light, as well as scattering processes to all orders in…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
There is a class of statistical problems that arises in several contexts, the Lattice QCD problem of particle physics being one that has attracted the most attention. In essence, the problem boils down to the estimation of an infinite…
In this paper we introduce a simple procedure for computing the macroscopic quantum behaviour of periodic quantum systems in the high energy regime. The macroscopic quantum coherence is ascribed to a one-particle state, not to a condensate…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
The use of quantum stochastic models is widespread in dynamical reduction, simulation of open systems, feedback control and adaptive estimation. In many applications only part of the information contained in the filter's state is actually…
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash…
By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68}, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
The quantum master equation is introduced for the density matrix representing Bogoliubov-BCS quasiparticles. A constraint to relate the loss and gain factors is taken into account to preserve the form of the density matrix. Such an equation…