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1. Localization lifetime of a many‐body system with periodic constructed disorder

   https://doi.org/10.1002/andp.201600366  

   Schecter, Michael; Shapiro, Michael; Dykman, Mark I. (March 2017, Annalen der Physik)

   We show that, in a many‐body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time‐domain formulation is complementary to the formulation of the many‐body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one‐dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations.image 

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2. Engineering Contactless Particle–Particle Interactions in Active Microswimmers

   https://doi.org/10.1002/adma.201703910  

   Nourhani, Amir; Brown, Daniel; Pletzer, Nicholas; Gibbs, John_G (November 2017, Advanced Materials)

   Abstract Artificial self‐propelled colloidal particles have recently served as effective building blocks for investigating many dynamic behaviors exhibited by nonequilibrium systems. However, most studies have relied upon excluded volume interactions between the active particles. Experimental systems in which the mobile entities interact over long distances in a well‐defined and controllable manner are valuable so that new modes of multiparticle dynamics can be studied systematically in the laboratory. Here, a system of self‐propelled microscale Janus particles is engineered to have contactless particle–particle interactions that lead to long‐range attraction, short‐range repulsion, and mutual alignment between adjacent swimmers. The unique modes of motion that arise can be tuned by modulating the system's parameters. 

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3. Proposal for many-body quantum chaos detection

   https://doi.org/10.1103/PhysRevResearch.7.013181  

   Das, Adway Kumar; Cianci, Cameron; Cabral, Delmar_G A; Zarate-Herrada, David A; Pinney, Patrick; Pilatowsky-Cameo, Saúl; Matsoukas-Roubeas, Apollonas S; Batista, Victor S; del_Campo, Adolfo; Torres-Herrera, E Jonathan; et al (February 2025, Physical Review Research)

   In this work, the term “quantum chaos” refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using, e.g., the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers. 

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4. A new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactors

   https://doi.org/10.1107/S2053273319008623  

   Hoeher, Alexandria; Mergelsberg, Sebastian; Borkiewicz, Olaf J.; Dove, Patricia M.; Michel, F. Marc (September 2019, Acta Crystallographica Section A Foundations and Advances)

   Structural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis. 

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5. Learning from many trajectories

   Tu, Stephen; Frostig, Roy; Soltanolkotabi, Mahdi (April 2024, Journal on Machine Learning Research)

   We initiate a study of supervised learning from many independent sequences ("trajectories") of non-independent covariates, reflecting tasks in sequence modeling, control, and reinforcement learning. Conceptually, our multi-trajectory setup sits between two traditional settings in statistical learning theory: learning from independent examples and learning from a single auto-correlated sequence. Our conditions for efficient learning generalize the former setting--trajectories must be non-degenerate in ways that extend standard requirements for independent examples. Notably, we do not require that trajectories be ergodic, long, nor strictly stable. For linear least-squares regression, given n-dimensional examples produced by m trajectories, each of length T, we observe a notable change in statistical efficiency as the number of trajectories increases from a few (namely m<=n) to many (namely m>=n). Specifically, we establish that the worst-case error rate of this problem is n/(mT) whenever m>=n. Meanwhile, when m<=n, we establish a (sharp) lower bound of n^2/(m^2T) on the worst-case error rate, realized by a simple, marginally unstable linear dynamical system. A key upshot is that, in domains where trajectories regularly reset, the error rate eventually behaves as if all of the examples were independent, drawn from their marginals. As a corollary of our analysis, we also improve guarantees for the linear system identification problem. 

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