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The Jordan-Wigner map in 2D is as an exact lattice regularization of the 2 pi-flux attachment to a hard-core boson (or spin-1/2) leading to a composite-fermion particle. When the spin-1/2 model obeys ice rules this map preserves locality,…
Anyons emerge as elementary excitations in low-dimensional quantum systems and exhibit behavior distinct from bosons or fermions. Previous models of anyons in one dimension (1D) are mainly categorized into two types: those that rely on…
We propose a model to show the self-assembling of network-like structures between a set of nodes without using preexisting positional information or long-range attraction of the nodes. The model is based on Brownian agents that are capable…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on…
The structure of self-bound one-dimensional droplets containing a mixture of Ytterbium fermionic isotopes ($^{173}$Yb, $^{171}$Yb) is calculated by means of a diffusion Monte Carlo technique. We considered only balanced setups in which all…
We exploit polarization self-rotation in atomic rubidium vapor to observe spontaneous symmetry breaking and bistability of polarization patterns. We pump the vapor cell with horizontally polarized light while the vertical polarization,…
Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and…
Experimental realizations of self-propelled colloidal Janus particles exploit the conversion of free energy into directed motion. One route are phoretic mechanisms that can be modeled schematically as the interconversion of two chemical…
An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…
We prove a generalized dynamical duality for identical particles in one dimension (1D). Namely, 1D systems with arbitrary statistics -- including bosons, fermions and anyons -- approach the same momentum distribution after long-time…
Circuit quantum electrodynamics systems are typically built from resonators and two-level artificial atoms, but the use of multi-level artificial atoms instead can enable promising applications in quantum technology. Here we present an…
An optimal control strategy is developed to construct nanostructures of desired geometry along line segments by means of directed self-assembly of charged particles. Such a control strategy determines the electric potentials of a set of…
Infants are experts at playing, with an amazing ability to generate novel structured behaviors in unstructured environments that lack clear extrinsic reward signals. We seek to mathematically formalize these abilities using a neural network…
Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Understanding the physical mechanisms that govern the formation of molecular complexes and…
In this paper we propose a biomolecular implementation of the push-down automaton (one of theoretical models of computing device with unbounded memory) using DNA molecules. The idea of this improved implementation was inspired by Cavaliere…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
We explore the dynamics of a one-dimensional lattice of state machines on two states and two symbols sequentially updated via a process of "reflexive composition." The space of 256 machines exhibits a variety of behavior, including…
Based on Brownian dynamics simulations we study the collective behavior of a twodimensional system of repulsively interacting colloidal particles, where each particle is propelled by a repulsive feedback force with time delay $\tau$.…
The result of a numerical simulation of two interacting particles in the framework of Nonunitary Newtonian Gravity is presented here. Particles are held close together by a 3-d harmonic trap and interact with each other via an `electrical'…