Related papers: Approximate but Accurate Quantum Dynamics from the…
We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…
An economic modeling approach for cavity quantum electrodynamics is provided by mean-field dynamics, wherein the optical field is described classically while a self-consistent interaction with quantum emitters is incorporated through the…
An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of…
The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its…
Reinforcement learning algorithms often require finiteness of state and action spaces in Markov decision processes (MDPs) (also called controlled Markov chains) and various efforts have been made in the literature towards the applicability…
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
It has been assumed that it is possible to approximate the interactions of quantized BPS solitons by quantising a dynamical system induced on a moduli space of soliton parameters. General properties of the reduction of quantum systems by a…
We have developed and implemented a self-consistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical LCAO basis set, which includes multiple-zeta and polarization orbitals. Exchange and…
The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series…
Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the…
The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach…
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations…
The Mori-Zwanzig projection formalism is widely used in studying systems with many degrees of freedom. We used a system-bath Hamiltonian system to show that the Mori's and Zwanzig's projection procedures are mutual limiting cases of each…
We design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for…
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both the electronic and the nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both…
In this work, we calculate the dynamic density correlations using Mori-Zwanzig-Nakajima projection operator method. With a judicious choice of slow variables we derive the evolution equations for these slow variables starting from…
A dynamical method for inelastic transport simulations in nanostructures is compared with a steady-state method based on non-equilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the…
We develop a waveform model to describe the inspiral, merger and ringdown of binary systems with comparable and intermediate mass-ratios. This model incorporates first-order conservative self-force corrections to the energy and angular…