The free energy landscape of mean field marginal glasses is ultrametric. We demonstrate that this feature remains in finite three dimensional systems by finding sets of minima which are nearby in configuration space. By calculating the distance between these nearby minima, we produce a small region of the distance metric. This metric exhibits a clear hierarchical structure and shows the signature of an ultrametric space. That such a hierarchy exists for the jamming energy landscape provides direct evidence for the existence of a marginal phase along the zero temperature jamming line.arXiv:1908.08159v2 [cond-mat.soft]
Preparation and spectroscopic characterization of Nd 3 + : Y 2 O 3 nanocrystals suspended in polymethyl methacrylateAbsorption intensities and emission cross section of intermanifold transition of Er 3 + in Er 3 + : Y 2 O 3 nanocrystals Optical absorption intensity analysis and emission cross sections for the intermanifold and the inter-Stark transitions of Nd 3 + ( 4 f 3 ) in polycrystalline ceramic Y 2 O 3Optical absorption and emission intensities are investigated for Nd 3+ in nanocrystalline Nd 3+: Y 2 O 3 . Room temperature absorption intensities of Nd 3+ ͑4f 3 ͒ transitions in synthesized Nd 3+: Y 2 O 3 nanocrystals have been analyzed using the Judd-Ofelt ͑J-O͒ approach to obtain the phenomenological intensity parameters. The J-O intensity parameters are used to calculate the spontaneous emission probabilities, radiative lifetimes, and branching ratios of the Nd 3+ transitions from the upper multiplet manifolds to the corresponding lower-lying multiplet manifolds 2S+1 L J of Nd 3+ ͑4f 3 ͒. The emission cross sections and room temperature fluorescence lifetimes of the important intermanifold 4 F 3/2 → 4 I J ͑J =9/ 2,11/ 2,13/ 2,15/ 2͒ transitions have been determined. We also compare the spectra of the Nd 3+ :Y 2 O 3 nanocrystals to those of the nanocrystals embedded in polymeric matrices of epoxy and chitosan, and we find similarities in terms of the detailed Stark energy levels of the Nd 3+ ion in the Y 2 O 3 nanocrystalline host. The 300 K spectra are analyzed for the energy ͑Stark͒ level transitions between the 2S+1 L J multiplet manifolds of Nd 3+ ͑4f 3 ͒. The results of this study are also compared with a crystal-field splitting analysis reported earlier for single-crystal Nd 3+ :Y 2 O 3 grown by a modified flame fusion method. We find that the spectroscopic properties of our nanocrystals embedded in polymeric hosts compare favorably with other ceramic and single-crystal forms of Nd 3+ :Y 2 O 3 currently available.
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