Related papers: Coarse-grained dynamics of ac-driven two-state sys…
Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control they may nevertheless exhibit simple dynamics approximately confined to a low-energy…
We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results…
We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…
We investigate the Magnus expansion for a generic time-dependent two-level system under single-axis driving.By virtue of the su(2) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate the usefulness of the…
We formulate an effective-description framework for the dynamics of open quantum systems by extending the time-coarse-graining formalism to open systems. Our coarse-graining procedure efficiently removes high-frequency processes which are…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is…
Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
We study the steady states and the coarsening dynamics in a one dimensional driven non-conserved system modelled by the so called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In…
Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant…
We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving…
In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained…
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…
Bottom-up coarse-grained molecular dynamics models are parameterized using complex effective Hamiltonians. These models are typically optimized to approximate high dimensional data from atomistic simulations. In contrast, human validation…
We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the…