Related papers: Vicinal Surfaces, Fractional Statistics and Univer…
In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…
A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a…
It has long been known that particles with short-range repulsive interactions in spatial dimension d=1 form universal quantum liquids in the low density limit: all properties can be related to those of the spinless free Fermi gas. Previous…
This paper investigates faceting mechanisms induced by electromigration in the regime where atomic steps are transparent. For this purpose we study several vicinal orientations by means of in-situ (optical diffraction, electronic…
Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
Let $N$ be a Riemannian, Lorentzian or neutral $4$-dimensional space form with constant sectional curvature $L_0$. In this paper, noticing the linearly dependent condition, we obtain characterizations of space-like surfaces in $N$ with flat…
A four dimensional description for the trigonal phase is presented. It has been demonstrated that it is possible to model one dimensional quasiperiodic structure with trigonal symmetry apart from recovering the Miller-Bravais scheme for the…
We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of…
Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
Long-ranged step-step attractions destabilize the vicinal crystal surfaces. Their competition with shorter-ranged step-step repulsions results in self-organized patterns. The exponent in the time-scaling of their characteristic size is…
With a Si(001) vicinal surface in mind, we study step wandering instability on a vicinal surface with an anisotropic surface diffusion whose orientation dependence alternates on each consecutive terrace. In a conserved system step wandering…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal…
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…
We examine a model of non-self-avoiding, fluctuating surfaces as a candidate continuum string theory of surfaces in three dimensions. This model describes Dynamically Triangulated Random Surfaces embedded in three dimensions with an…