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Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence…
Strongly correlated materials exhibit exotic electronic states arising from the strong correlation between electrons. Dimensionality provides a tuning knob because thinning down to atomic thickness reduces screening effects and enhances…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D-confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical…
Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on…
The approach for the description of the DNA conformational transformations on the mesoscopic scales in the frame of the double helix is presented. Due to consideration of the joint motions of DNA structural elements along the conformational…
A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a…
This is a revised form of the previous paper in which we study cones of positive maps of B(H) into itself. We add the result that the dual cone of a symmetric mapping cone is itself a symmetric mapping cone. As applications we obtain…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Electron doping is an excellent tuning knob to explore different phases of matter in two-dimensional (2D) materials. For example, tuning the Fermi level at a van Hove singularity in twisted bilayer graphene can enhance electron-electron…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…
Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…
We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are given, primarily on questions concerning the stability of…
Fabrication of custom-built heterostructures based on stacked 2D materials provides an effective method to controllably tune electronic and optical properties. To that end, optimizing fabrication techniques for building these…
We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one-dimension.…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
As a continuation of \cite{NSY:local}, we mainly discuss the global structure of two-dimensional locally compact geodesically complete metric spaces with curvature bounded above. We first obtain the result on the Lipschitz homotopy…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…