Related papers: Jamming I: A volume function for jammed matter
A new first-principles statistical mechanics formulation is proposed to describe slow and dilated granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts, where all the important physics takes place,…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Wannier functions have widespread utility in condensed matter physics and beyond. Topological physics, on the other hand, has largely involved the related notion of compactly-supported Wannier-type functions, which arise naturally in flat…
We compute structure functions in the Hamiltonian formalism on a momentum lattice using a physically motivated regularisation that links the maximal parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that our method…
We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the…
Take a set of balls in $\mathbb R^d$. We find a subset of pairwise disjoint balls whose combined perimeter controls the perimeter of the union of the original balls. This can be seen as a boundary version of the Vitali covering lemma. We…
We derive explicit expressions for the volume elements of both the minimal and maximal monotone metrics over the (n^{2} - 1)-dimensional convex set of n x n density matrices for the cases n = 3 and 4. We make further progress for the…
Let $\mathcal{P}_{\lambda}:=\mathcal{P}_{\lambda\kappa}$ denote a Poisson point process of intensity $\lambda\kappa$ on $[0,1]^d,d\geq2$, with $\kappa$ a bounded density on $[0,1]^d$ and $\lambda\in(0,\infty)$. Given a closed subset…
Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity…
We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset…
In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
Let $X$ be a Poisson point process and $K\subset\mathbb{R}^d$ a measurable set. Construct the Voronoi cells of all points $x\in X$ with respect to $X$, and denote by $v_X(K)$ the union of all Voronoi cells with nucleus in $K$. For $K$ a…
We investigate the entanglement entropy in quantum states featuring repeated sequential excitations of unit patterns in momentum space. In the scaling limit, each unit pattern contributes independently and universally to the entanglement…
Soft, disordered, micro-structured materials are ubiquitous in nature and industry, and are different from ordinary fluids or solids, with unusual, interesting static and flow properties. The transition from fluid to solid -at the so-called…
Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is $\CP^1$ and the function is a polynomial, we give an…
We present a deterministic polynomial-time algorithm for estimating the volume of a hypercube intersected by a fixed number of constraints of the type $f(x) \leq b$, where $f$ is the sum of univariate functions that are each nonnegative,…
In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards'…