Related papers: A local orientational order parameter for systems …
The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor coupling is used to construct a system of floating particles characterized by motifs of up to six consecutive local spins. The spin couplings cause the assembly…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. We generalize…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
Geometrically nontrivial quantum states can be defined as states that cannot be prepared by a constant depth geometrically local unitary circuit starting from a product state. However, for topological phases, as well as a large class of…
In crystalline solids, the electronic polarization follows the \emph{generalized Neumann's principle}, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry…
Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite…
We formulate a general family of entanglement criteria for multipartite systems. Fisher information criteria compare the sensitivity to unitary rotations with the variances of suitable local observables. Generalized squeezing-type criteria…
In pursuit of a minimal basis for systems with non-ideal bond angles, in this work we try to pinpoint the exact orientation of the major overlapping orbitals along the nearest neighbouring coordination segments in a given system such that…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a…
Many proposals have already been made for realizing programmable matter, ranging from shape-changing molecules, DNA tiles, and synthetic cells to reconfigurable modular robotics. Envisioning systems of nano-sensors devices, we are…
We calculate the configurational entropy of hard particles confined in a cavity using Monte Carlo integration. Multiple combinations of particle and cavity shapes are considered. For small numbers of particles $N$, we show that the entropy…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation…
Machine learning methods are being explored in many areas of science, with the aim of finding solution to problems that evade traditional scientific approaches due to their complexity. In general, an order parameter capable of identifying…
We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual…