Related papers: Reduced Dynamics of Full Counting Statistics
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
The reduced dynamics formalism has recently emerged as a powerful tool to study the dynamics of non-equilibrium quantum impurity models in strongly correlated regimes. Examples include the non-equilibrium Anderson impurity model near the…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
Non-equilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady state non-equilibrium transport…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Employing a recently developed method that is numerically accurate within a model space simulating the real-time dynamics of few-body systems interacting with macroscopic environmental quantum fields, we analyze the full dynamics of an…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…