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1. Many-Body Resonances in the Avalanche Instability of Many-Body Localization

   https://doi.org/10.1103/PhysRevLett.130.250405  

   Ha, Hyunsoo; Morningstar, Alan; Huse, David A. (June 2023, Physical Review Letters)

   Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called “avalanche,” where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems. 

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2. The many facets of shape

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3. The Many Ways to Invisible

   Anderson, Gregory_D_S (November 2023, Journal of the Southeast Asian Linguistics Society)

   Sidwell, Paul; Alves, Mark (Ed.)

   How Sora uses older morphology of prefixation, infixation and reduplication to create more than two dozen forms that mean 'invisible'. The morphology is largely old and inherited from Austroasiatic. 

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4. The power of many colours

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   Alon, Noga; Bucić, Matija; Christoph, Micha; Krivelevich, Michael (January 2024, Forum of Mathematics, Sigma)

   A classical problem, due to Gerencsér and Gyárfás from 1967, asks how large a monochromatic connected component can we guarantee in any r-edge colouring of Kn? We consider how big a connected component can we guarantee in any r-edge colouring of Kn if we allow ourselves to use up to s colours. This is actually an instance of a more general question of Bollobás from about 20 years ago which asks for a k-connected subgraph in the same setting. We complete the picture in terms of the approximate behaviour of the answer by determining it up to a logarithmic term, provided n is large enough. We obtain more precise results for certain regimes which solve a problem of Liu, Morris and Prince from 2007, as well as disprove a conjecture they pose in a strong form. We also consider a generalisation in a similar direction of a question first considered by Erdős and Rényi in 1956, who considered given n and m, what is the smallest number of m-cliques which can cover all edges of Kn? This problem is essentially equivalent to the question of what is the minimum number of vertices that are certain to be incident to at least one edge of some colour in any r-edge colouring of Kn. We consider what happens if we allow ourselves to use up to s colours. We obtain a more complete understanding of the answer to this question for large n, in particular determining it up to a constant factor for all 1≤s≤r, as well as obtaining much more precise results for various ranges including the correct asymptotics for essentially the whole range. 

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5. Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach

   https://doi.org/10.1063/1.5125802  

   Veccham, Srimukh Prasad; Lee, Joonho; Head-Gordon, Martin (November 2019, The Journal of Chemical Physics)