metadata
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