Related papers: Non-Perturbative Quantum Dynamical Decoupling
A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et…
This paper presents a nonlinear model predictive control strategy for stochastic systems with general (state and input dependent) disturbances subject to chance constraints. Our approach uses an online computed stochastic tube to ensure…
We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that…
Recent studies of the dynamically assisted Schwinger effect have shown that particle production is significantly enhanced by a proper choice of the electric field. We demonstrate that optimal control theory provides a systematic means of…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
The recently developed formalism of Markovian master equations for quantum open systems with external periodic driving is applied to the theory of dynamical decoupling by periodic control. This new approach provides a more detailed…
This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic,…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
This article addresses the problem of data-driven numerical optimal control for unknown nonlinear systems. In our scenario, we suppose to have the possibility of performing multiple experiments (or simulations) on the system. Experiments…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
We present a theoretical proposal for preparing and manipulating a state of a single continuous-variable degree of freedom confined to a nonharmonic potential. By utilizing optimally controlled modulation of the potential's position and…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…