Related papers: A Hybrid Algorithm for Systems of Non-interacting …
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction:…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization…
Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
To exclude collisions leading to the overlap of finite-sized charged particles in molecular dynamics (MD) simulations in systems like complex (dusty) plasmas, we developed a scheme to generate a pair interaction force functionally depending…
We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment…
The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based…
In this Ph.D. thesis dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. The research is neither restricted to static properties or long-term relaxation evolutions nor does it…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
We study an additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics, which is proposed as an approximate model to the fluctuating hydrodynamics of chemotactically interacting particles around their mean-field limit. As such, the…
We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear term in the Ohta-Kawasaki free energy functional, we show that the…
We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the…