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1. Engineering the glass structure of a discotic liquid crystal by multiple kinetic arrests

   https://doi.org/10.1063/5.0149886  

   Yu, Junguang; Chen, Zhenxuan; Fatina, Caroline; Chatterjee, Debaditya; Bock, Harald; Richert, Ranko; Voyles, Paul; Ediger, M. D.; Yu, Lian (May 2023, The Journal of Chemical Physics)

   X-ray scattering has been used to characterize the columnar packing and the π stacking in a glass-forming discotic liquid crystal. In the equilibrium liquid state, the intensities of the scattering peaks for π stacking and columnar packing are proportional to each other, indicating concurrent development of the two orders. Upon cooling into the glassy state, the π–π distance shows a kinetic arrest with a change in the thermal expansion coefficient (TEC) from 321 to 109 ppm/K, while the intercolumnar spacing exhibits a constant TEC of 113 ppm/K. By changing the cooling rate, it is possible to prepare glasses with a wide range of columnar and π stacking orders, including zero order. For each glass, the columnar order and the π stacking order correspond to a much hotter liquid than its enthalpy and π–π distance, with the difference between the two internal (fictive) temperatures exceeding 100 K. By comparison with the relaxation map obtained by dielectric spectroscopy, we find that the δ mode (disk tumbling within a column) controls the columnar order and the π stacking order trapped in the glass, while the α mode (disk spinning about its axis) controls the enthalpy and the π–π spacing. Our finding is relevant for controlling the different structural features of a molecular glass to optimize its properties. 

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2. Complex analytic dependence on the dielectric permittivity in ENZ materials: The photonic doping example

   https://doi.org/10.1002/cpa.22138  

   Kohn, Robert V.; Venkatraman, Raghavendra (September 2023, Communications on Pure and Applied Mathematics)

   Abstract Motivated by the physics literature on “photonic doping” of scatterers made from “epsilon‐near‐zero” (ENZ) materials, we consider how the scattering of time‐harmonic TM electromagnetic waves by a cylindrical ENZ region is affected by the presence of a “dopant” in which the dielectric permittivity is not near zero. Mathematically, this reduces to analysis of a 2D Helmholtz equation  with a piecewise‐constant, complex valued coefficientathat is nearly infinite (say with ) in . We show (under suitable hypotheses) that the solutionudepends analytically on δ near 0, and we give a simple PDE characterization of the terms in its Taylor expansion. For the application to photonic doping, it is the leading‐order corrections in δ that are most interesting: they explain why photonic doping is only mildly affected by the presence of losses, and why it is seen even at frequencies where the dielectric permittivity is merely small. Equally important: our results include a PDE characterization of the leading‐order electric field in the ENZ region as , whereas the existing literature on photonic doping provides only the leading‐order magnetic field. 

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3. Tunable layered-magnetism–assisted magneto-Raman effect in a two-dimensional magnet CrI ₃

   https://doi.org/10.1073/pnas.2012980117  

   Jin, Wencan; Ye, Zhipeng; Luo, Xiangpeng; Yang, Bowen; Ye, Gaihua; Yin, Fangzhou; Kim, Hyun Ho; Rojas, Laura; Tian, Shangjie; Fu, Yang; et al (October 2020, Proceedings of the National Academy of Sciences)

   null (Ed.)

   We used a combination of polarized Raman spectroscopy experiment and model magnetism–phonon coupling calculations to study the rich magneto-Raman effect in the two-dimensional (2D) magnet CrI 3 . We reveal a layered-magnetism–assisted phonon scattering mechanism below the magnetic onset temperature, whose Raman excitation breaks time-reversal symmetry, has an antisymmetric Raman tensor, and follows the magnetic phase transitions across critical magnetic fields, on top of the presence of the conventional phonon scattering with symmetric Raman tensors in N -layer CrI 3 . We resolve in data and by calculations that the first-order A g phonon of the monolayer splits into an N -fold multiplet in N -layer CrI 3 due to the interlayer coupling ( N ≥ 2 ) and that the phonons within the multiplet show distinct magnetic field dependence because of their different layered-magnetism–phonon coupling. We further find that such a layered-magnetism–phonon coupled Raman scattering mechanism extends beyond first-order to higher-order multiphonon scattering processes. Our results on the magneto-Raman effect of the first-order phonons in the multiplet and the higher-order multiphonons in N -layer CrI 3 demonstrate the rich and strong behavior of emergent magneto-optical effects in 2D magnets and underline the unique opportunities of spin–phonon physics in van der Waals layered magnets. 

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4. Small circle expansion for adjoint QCD2 with periodic boundary conditions

   https://doi.org/10.1007/JHEP11(2024)128  

   Dempsey, Ross; Klebanov, Igor R; Pufu, Silviu S; Søgaard, Benjamin T (November 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We study 1 + 1-dimensional SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumferenceL. Using periodic boundary conditions, we derive the effective action for the quantum mechanics of the holonomy and the fermion zero modes in perturbation theory up to order (gL)³. When the adjoint fermion mass-squared is tuned tog²N/(2π), the effective action is found to be an example of supersymmetric quantum mechanics with a nontrivial superpotential. We separate the states into theℤ_Ncenter symmetry sectors (universes) labeled byp= 0, . . . ,N– 1 and show that in one of the sectors the supersymmetry is unbroken, while in the others it is broken spontaneously. These results give us new insights into the (1, 1) supersymmetry of adjoint QCD₂, which has previously been established using light-cone quantization. When the adjoint mass is set to zero, our effective Hamiltonian does not depend on the fermions at all, so that there are 2^N−1degenerate sectors of the Hilbert space. This construction appears to provide an explicit realization of the extended symmetry of the massless model, where there are 2^2N−2operators that commute with the Hamiltonian. We also generalize our results to other gauge groupsG, for which supersymmetry is found at the adjoint mass-squaredg²h^∨/(2π), whereh^∨is the dual Coxeter number ofG. 

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5. Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

   https://doi.org/10.5194/npg-24-481-2017  

   Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C. (January 2017, Nonlinear Processes in Geophysics)

   Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence. 

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