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