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--- |
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license: bigscience-openrail-m |
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widget: |
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- text: I am totally a human, trust me bro. |
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example_title: default |
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- text: >- |
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This study presents a comprehensive analytical investigation of the |
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collective excitation branch in the continuum of pair-condensed Fermi gases, |
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with a focus on identifying and establishing scaling laws for this |
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phenomenon. Based on thorough theoretical analysis and simulations, we |
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demonstrate that collective excitations in pair-condensed Fermi gases |
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exhibit distinct scaling behaviors, characterized by universal scaling |
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exponents that are independent of the particular system parameters. Our |
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findings suggest that these scaling laws reflect the underlying symmetries |
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and correlations of these systems, and thus can provide valuable insights |
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into their microscopic properties. Moreover, we demonstrate that the |
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collective excitation branch in pair-condensed Fermi gases can provide a |
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robust signature for the presence of pairing correlations, which can be |
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detected experimentally through various spectroscopic techniques. |
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Additionally, we explore the implications of our results for ongoing |
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experimental efforts aimed at studying collective excitations in these |
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systems, highlighting the potential for using collective excitations as a |
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probe of the pairing mechanism and providing a bridge between theory and |
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experiment. Overall, our study sheds new light on the collective behavior of |
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Fermi gases with pairing correlations, and identifies key features that can |
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be used to further explore their physics, both theoretically and |
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experimentally. These findings represent a significant contribution to the |
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field of condensed matter physics, and open up new avenues for investigating |
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the behavior of strongly correlated systems in general. |
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example_title: generated1 |
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- text: >- |
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On Zariski Main Theorem in Algebraic Geometry and Analytic Geometry. We fill |
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a surprising gap of Complex Analytic Geometry by proving the analogue of |
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Zariski Main Theorem in this geometry, i.e. proving that an holomorphic map |
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from an irreducible analytic space to a normal irreducible one is an open |
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embedding if and only if all its fibers are discrete and it induces a |
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bimeromorphic map on its image. We prove more generally the "Generalized |
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Zariski Main Theorem for analytic spaces", which claims that an holomorphic |
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map from an irreducible analytic space to a irreducible locally irreducible |
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one is an open embedding if and only if it is flat and induces a |
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bimeromorphic map on its image. Thanks to the "analytic criterion of |
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regularity" of Serre-Samuel in GAGA [12] and to "Lefschetz Principle", we |
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finally deduce the "Generalized Zariski Main Theorem for algebraic varieties |
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of characteristical zero", which claims that a morphism from such an |
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irreducible variety to an irreducible unibranch one is an open immersion if |
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and only if it is birational and flat. |
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example_title: real1 |
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datasets: |
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- NicolaiSivesind/human-vs-machine |
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language: |
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- en |
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pipeline_tag: text-classification |
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tags: |
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- mgt-detection |
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- ai-detection |
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--- |
