Related papers: Adaptive Resummation of Markovian Quantum Dynamics
We give a number of results on approximations of Markov kernels in total variation and Wasserstein norms weighted by a Lyapunov function. The results are applied to examples from Bayesian statistics where approximations to transition…
An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of…
Fully kinetic simulations of the Vlasov equation require a careful numerical treatment of phase space advections to ensure accuracy and stability in six dimensions. To test the accuracy of full Vlasov codes, we have developed a surprisingly…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
We present two different approaches towards the Landau-Zener problem: (i) The Markov approximation in the integro-differential equation for one of the two probability amplitudes, and (ii) an amplitude-and-phase analysis of the linear second…
We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative quantum impurity models. These are small open quantum systems with interaction and local Markovian dissipation, coupled to a large quantum bath. Our…
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good…
Dynamics of non-Markovian systems is a classic problem yet it attracts an everlasting activity in physics and beyond. A powerful tool for modeling such setups is the Generalized Langevin Equation, however, its analysis typically poses a…
A systematic first-order correction to the standard Markov master equation for open quantum systems interacting with a bosonic bath is presented. It extends the Markov Lindblad master equation to the more general case of non-Markovian…
In this paper, We propose a general Riemannian proximal optimization algorithm with guaranteed convergence to solve Markov decision process (MDP) problems. To model policy functions in MDP, we employ Gaussian mixture model (GMM) and…
We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on…
We derive a family of Gaussian non-Markovian stochastic Schr\"odinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different…
Even though Nearest Neighbor Gaussian Processes (NNGP) alleviate considerably MCMC implementation of Bayesian space-time models, they do not solve the convergence problems caused by high model dimension. Frugal alternatives such as response…
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…