Related papers: Nonlocal Potentials and Crystalline Order in One a…

Quasi-long ranged order is the hallmark of two-dimensional liquid crystals. At equilibrium, this property implies that the correlation function of the local orientational order parameter decays with distance as a power law: i.e.…

Quantum theory in a global space-time gives rise to non-local correlations, which cannot be explained causally in a satisfactory way; this motivates the study of theories with reduced global assumptions. Oreshkov, Costa, and Brukner (2012)…

We propose a definition for topological order at nonzero temperature in analogy to the usual zero temperature definition that a state is topologically ordered, or "nontrivial", if it cannot be transformed into a product state (or a state…

So-called polar liquid crystals possess spontaneous long-range mutual orientation of their electric dipole moments, conferring bulk polarity to fluid phases of matter. The combination of polarity and fluidity leads to complex phase…

A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on…

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions.…

We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schr\"odinger equation in polar coordinates, 2. They allow an…

Domain boundaries and other twin boundaries in crystalline materials are receiving increasing interest. They can carry unique functional properties, which in many cases are absent in the surrounding bulk material. One such property of…

We consider unambiguous discrimination of two separable bipartite states, one being pure and the other being a rank-2 mixed state. There is a gap between the optimal success probability under global measurements and the one achieved by…

We propose a measure of non-classical correlations in bipartite quantum states based on local unitary operations. We prove the measure is non-zero if and only if the quantum discord is non-zero; this is achieved via a new characterization…

This paper summarises a numerical investigation of the statistical properties of orbits evolved in `frozen,' time-independent N-body realisations of smooth, time-independent density distributions, allowing for 10^(2.5)<N<10^(5.5). Two…

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition…

We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…

We prove that recent theorems of non-locality without inequalities are not effective, for systems of two spacelike separated 2-level sub-systems, in proving non-locality of any empirically valid theory sharing a set of correlations with…

We generalise the two-sided Bogoliubov inequality for classical particles from [L. Delle Site et al., J.Stat.Mech.Th.Exp. 083201 (2017)] to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower…

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose…

We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity…

Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar…

The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes…

The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally…