Related papers: A Divide-and-Conquer Algorithm for Disordered and …
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
We investigate the impact of random pinned disorder on a collection of self propelled particles. To achieve this, we construct a continuum model by formulating the coupled hydrodynamic equations for slow variables, local density and…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We consider a particle in one dimension submitted to amplitude and phase disorder. It can be mapped onto the complex Burgers equation, and provides a toy model for problems with interplay of interferences and disorder, such as the NSS model…
We propose a decentralized subspace algorithm for identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
In this paper, we study a class of set cover problems that satisfy a special property which we call the {\em small neighborhood cover} property. This class encompasses several well-studied problems including vertex cover, interval cover,…
A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted…
In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x)…
The localization in a disordered system of $N$ interacting spins coupled by the long-range anisotropic interaction $1/R^{\alpha}$ is investigated using a finite size scaling in a $d=1$ -dimensional system for $N=8, 10, 12, 14$. The results…