Related papers: Unravelling mean-field Lindblad equation
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…
We employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of microscopic subregion both in spin and fermionic many-body systems. We exemplify our method by…
The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health…
In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schr\"odinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…
In the mean-field regime, we prove convergence (with explicit bounds) of the many-body von Neumann dynamics with bounded interactions to the Hartree-von Neumann dynamics.
We present a new implementation of the Monte Carlo method to simulate the evolution of star clusters. The major improvement with respect to the previously developed codes is the treatment of the external tidal field taking into account for…
We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain…
We offer in this short report a simple Monte-Carlo method for solving a well-posed non-linear integral equations of second Fredholm's and Volterra's type and built a confidence region for solution in an uniform norm, applying the grounded…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
In this work, we study the correlation between entanglement and the negative sign problem in quantum Monte Carlo for the simulation of low-dimensional strongly correlated quantum many body systems. Entanglement entropy characterizes the…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…
The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for $N$-particle…
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to…
Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an…
We study a trapped system of fermions with a zero-range two-body interaction using the shell-model Monte Carlo method, providing {\em ab initio} results for the low particle number limit where mean-field theory is not applicable. We present…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…