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1. Etale and crystalline companions, I

   https://doi.org/10.46298/epiga.2022.6820  

   Kedlaya, Kiran S. (December 2022, Épijournal de Géométrie Algébrique)

   Let $$X$$ be a smooth scheme over a finite field of characteristic $$p$$.Consider the coefficient objects of locally constant rank on $$X$$ in $$\ell$$-adicWeil cohomology: these are lisse Weil sheaves in \'etale cohomology when $$\ell\neq p$$, and overconvergent $$F$$-isocrystals in rigid cohomology when $$\ell=p$$.Using the Langlands correspondence for global function fields in both the\'etale and crystalline settings (work of Lafforgue and Abe, respectively), onesees that on a curve, any coefficient object in one category has "companions"in the other categories with matching characteristic polynomials of Frobeniusat closed points. A similar statement is expected for general $$X$$; building onwork of Deligne, Drinfeld showed that any \'etale coefficient object has\'etale companions. We adapt Drinfeld's method to show that any crystallinecoefficient object has \'etale companions; this has been shown independently byAbe--Esnault. We also prove some auxiliary results relevant for theconstruction of crystalline companions of \'etale coefficient objects; thissubject will be pursued in a subsequent paper. 

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2. Stable polynomials and crystalline measures

   https://doi.org/10.1063/5.0012286  

   Kurasov, P.; Sarnak, P. (August 2020, Journal of Mathematical Physics)

   Explicit examples of positive crystalline measures and Fourier quasicrystals are constructed using pairs of stable polynomials, answering several open questions in the area. 

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3. Crystalline Quantum Circuits

   https://doi.org/10.1103/PRXQuantum.4.030313  

   Sommers, Grace M.; Huse, David A.; Gullans, Michael J. (July 2023, PRX Quantum)

   Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in deterministic circuits with similar applications, we construct classes of nonrandom unitary Clifford circuits by imposing translation invariance in both time and space. Further imposing dual unitarity, our circuits effectively become crystalline spacetime lattices whose vertices are swap or iswap two-qubit gates and whose edges may contain one-qubit gates. One can then require invariance under (subgroups of) the crystal’s point group. Working on the square and kagome lattices, we use the formalism of Clifford quantum cellular automata to describe operator spreading, entanglement generation, and recurrence times of these circuits. A full classification on the square lattice reveals, of particular interest, a “nonfractal good scrambling class” with dense operator spreading that generates codes with linear contiguous code distance and high performance under erasure errors at the end of the circuit. We also break unitarity by adding spacetime translation-invariant measurements and find a class of such circuits with fractal dynamics. 

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4. Asymmetric Molecular Dynamics and Anisotropic Phase Separation in the Cocrystal of the Crystalline/Crystalline Polymer Blend

   https://doi.org/10.1021/acsmacrolett.1c00745  

   Zheng, Ying; Kafle, Navin; Schwarz, Derek; Eagan, James M.; Hayano, Shigetaka; Nakama, Yuki; Pan, Pengju; Miyoshi, Toshikazu (February 2022, ACS Macro Letters)
5. Crystalline–Amorphous Nanostructures: Microstructure, Property and Modelling

   https://doi.org/10.3390/ma16072874  

   Wei, Bingqiang; Li, Lin; Shao, Lin; Wang, Jian (April 2023, Materials)

   Crystalline metals generally exhibit good deformability but low strength and poor irradiation tolerance. Amorphous materials in general display poor deformability but high strength and good irradiation tolerance. Interestingly, refining characteristic size can enhance the flow strength of crystalline metals and the deformability of amorphous materials. Thus, crystalline–amorphous nanostructures can exhibit an enhanced strength and an improved plastic flow stability. In addition, high-density interfaces can trap radiation-induced defects and accommodate free volume fluctuation. In this article, we review crystalline–amorphous nanocomposites with characteristic microstructures including nanolaminates, core–shell microstructures, and crystalline/amorphous-based dual-phase nanocomposites. The focus is put on synthesis of characteristic microstructures, deformation behaviors, and multiscale materials modelling. 

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