相关论文: Proof of Aperiodicity of hat tile using the Golden…
Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. We show how this basic geometric property gives rise to a new topology in band insulators. We study spatial symmetries that translate the origin…
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…
A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a $O(n\log^2{n})$-time algorithm for deciding if a…
A plethora of unconventional localization phenomena and fractal features of linear spectrum observed in quasiperiodic structures have been accompanied by a long-standing quest for the geometrical elements and structures that permit tilings…
We investigate a Schwarzschild metric exhibiting a signature change across the event horizon, which gives rise to what we term a Lorentzian-Euclidean black hole. The resulting geometry is regularized by employing the Hadamard partie finie…
It is proved that homeomorphic images of certain two-dimensional aperiodic tilings, such as Ammann-A2 tilings, are recognizable, in both mathematical and practical senses. One implication of the results is that it is possible to search for…
Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which…
We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\mathsf{O}(3)\times\mathsf{O}(10)$ on $S^{12}\subset \mathbb{R}^{13}= \mathbb{R}^3\oplus \mathbb{R}^{10}$. The…
Moir\'e patterns of twisted and scaled bilayers have recently emerged as a fertile source of quasiperiodic order in two-dimensional materials. Inspired by these systems, we introduce the \emph{near-coincidence method} for generating…
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in…
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General…
The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…
Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by…
We investigate a symmetry protected $Z_2$ topological electron glass -- a glassy equivalent of the $Z_2$ topological band insulator in crystalline systems -- and uncover associated quantum phase transitions in this three dimensional…
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
We study here slopes of periodicity of tilings. A tiling is of slope if it is periodic along direction but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they…
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…
Einstein-aether gravity is a theory that breaks the local Lorentz symmetry by introducing a preferred direction via a vector field, which is considered to play the role of an aether. The theory is identified by four coupling constants…
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both…