Related papers: A Global Crystalline Period Map
A new method for characterization of periodically poled crystals is developed based on spontaneous parametric down-conversion. The method is demonstrated on crystals of Y:LiNbO3, Mg:Y:LiNbO3 with non-uniform periodically poled structures,…
The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
For every compact Kaehler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan equation in the algebra of polyvector fields. Our construction involves the notion…
Time crystalline structures can be created in periodically driven systems. They are temporal lattices which can reveal different condensed matter behaviours ranging from Anderson localization in time to temporal analogues of many-body…
Abstractions of crystalline materials known as periodic body-and-bar frameworks are made of rigid bodies connected by fixed-length bars and subject to the action of a group of translations. In this paper, we give a Maxwell-Laman…
We propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
The response of a tunable photonic oscillator, consisting of an Optically Injected Semiconductor Laser, under an injected Frequency Comb is considered with the utilization of the concept of the Time Crystal that has been widely used for the…
Graph neural networks are widely used in machine learning applied to chemistry, and in particular for material science discovery. For crystalline materials, however, generating graph-based representation from geometrical information for…
We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…
For certain complex projective manifolds (such as K3 surfaces and their higher dimensional analogues, the complex symplectic projective manifolds) the period map takes values in a locally symmetric variety of type IV. It is often an open…
The notion of a cyclic map g: A -> X is a natural generalization of a Gottlieb element in pi_n(X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which…
A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the…
In the paper we present a proof of the local criterion for crystalline structures which generalizes the local criterion for regular systems. A Delone set is called a crystal if it is invariant with respect to a crystallgraphic group.…
This paper studies the derived de Rham cohomology of F_p and p-adic schemes, and is inspired by Beilinson's recent work. Generalising work of Illusie, we construct a natural isomorphism between derived de Rham cohomology and crystalline…
A general problem is to classify the real forms of a complex variety up to isomorphism. This paper introduces the polar group of a real form $X$ of a complex variety $Y$ as a tool to distinguish such real forms. This group is an invariant…
We give a new solution of the "homotopy periods" problem, as highlighted by Sullivan, which places explicit geometrically meaningful formulae first dating back to Whitehead in the context of Quillen's formalism for rational homotopy theory…
Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures…
Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of…