Related papers: Tiling with almost-BPS states
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices, and…
We present BPS solutions to a general class of Wess-Zumino models which extend previous results in the literature. We discuss their relation to amplitudes on threshold, and their application to scalar domain walls in Supersymmetric QCD. We…
I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the…
The infinite discrete stable Boltzmann maps are generalisations of the well-known Uniform Infinite Planar Quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is…
We study BPS saturated objects with axial geometry (wall junctions, vortices) in generalized Wess-Zumino models. It is observed that the tension of such objects is negative in general (although ``exceptional'' models are possible). We show…
We construct BPS states in the matrix description of M-theory. Starting from a set of basic M-theory branes, we study pair intersections which preserve supersymmetry. The fractions of the maximal supersymmetry obtained in this way are 1/2,…
Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects…
In the paper we study the structure of hyperplanes of so called binomial partial Steiner triple systems (BSTS's, in short) i.e. of configurations with $\binom{n}{2}$ points and $\binom{n}{3}$ lines, each line of the size $3$. Consequently,…
We discuss quantum tunneling between classically BPS saturated solitons in two-dimensional theories with N=2 supersymmetry and a compact space dimension. Genuine BPS states form shortened multiplets of dimension two. In the models we…
Twisted states with non-zero winding numbers composed of sinusoidally coupled identical oscillators have been observed in a ring. The phase of each oscillator in these states constantly shifts, following its preceding neighbor in a…
In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…
We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have…
We study the possible BPS domain wall junction configurations for general polynomial superpotentials of N=1 supersymmetric Wess-Zumino models in D=4. We scan the parameter space of the superpotential and find different possible BPS states…
Non-supersymmetric multi-wall configurations are generically unstable. It is proposed that the stabilization in compact space can be achieved by introducing a winding number into the model. A BPS-like bound is studied for the energy of…
We introduce and classify nonequivalent commensurate stackings for bilayer dice or $\mathcal{T}_3$ lattice. For each of the four stackings with vertical alignment of sites in two layers, a tight-binding model and an effective model…
We introduce a class of states so-called semi-SSPPT (semi super strong positive partial transposition) states in infinite-dimensional bipartite systems by the Cholesky decomposition in terms of operator matrices and show that every…
We report the existence of quasi-bound modes in the continuum (quasi-BICs) in architected elastic plates based on a square lattice. The structure consists of topologically trivial and nontrivial lattices, forming an interface and…
Suppose L and M are full-rank lattices in Euclidean space, such that vol(L) < vol(M). Answering a question of Han and Wang from 2001, we show how to construct a bounded measurable set F (we can even take F to be a finite union of polytopes)…
We describe the translation invariant stationary states (TIS) of the one-dimensional facilitated asymmetric exclusion process in continuous time, in which a particle at site $i\in\mathbb{Z}$ jumps to site $i+1$ (respectively $i-1$) with…
We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space…