Related papers: A Divide-and-Conquer Algorithm for Disordered and …
Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then…
Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are…
Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…
The interplay between the quantum interferences responsible for one particle localization over a length L_1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over…
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to…
Given a rectangle $R$ with area $A$ and a set of areas $L=\{A_1,...,A_n\}$ with $\sum_{i=1}^n A_i = A$, we consider the problem of partitioning $R$ into $n$ sub-regions $R_1,...,R_n$ with areas $A_1,...,A_n$ in a way that the total…
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…
Localization in interacting systems caused by disorder, known as many-body localization (MBL), has attracted a lot of attention in recent years. Most systems studied in this context also show single-particle localization, and the question…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two…
Confocal microscopy of colloids combined with digital image processing has become a powerful tool in soft matter physics and materials science. Together, these techniques enable locating and tracking of more than half a million individual…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of $\ell$-bits, a set…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the…