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Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects…
Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-$S$ system weakly coupled to a bosonic bath. The complete tomographic knowledge about the…
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution…
We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations,…
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…
We consider the time evolution of systems in which a spatially homogeneous scalar field is coupled to fermions. The quantum back-reaction is taken into account in one-loop approximation. We set up the basic equations and their…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…
A number of non-Markovian stochastic Schr\"odinger equations, ranging from the numerically exact hierarchical form towards a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited…
We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
We introduce an exact open system method to describe the dynamics of quantum systems that are strongly coupled to specific types of environments comprising of spins, such as central spin systems. Our theory is similar to the established…
We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…
The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
We construct a broad class of completely positive maps and Go\-rini--Kossakowski--Sudarshan-Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit…