Related papers: Packing, coding, and ground states
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…
In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric…
We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in $\mathbb{R}^d$ that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
This perspective will overview an emerging paradigm for self-organized soft materials, {\it geometrically-frustrated assemblies}, where interactions between self-assembling elements (e.g. particles, macromolecules, proteins) favor local…
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…
Our understanding of supercooled liquids and glasses has lagged significantly behind that of simple liquids and crystalline solids. This is in part due to the many possibly relevant degrees of freedom that are present due to the disorder…
It has been known for some time now that error correction plays a fundamental role in the determining the emergence of semiclassical geometry in quantum gravity. In this work I connect several different lines of reasoning to argue that this…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
Physical properties of materials are seldom studied in the context of packing problems. In this work we study the behavior of semifluids: materials with particular characteristics, that share properties both with solids and with fluids. We…
Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…