The curious case of operators with spectral density increasing as $Ω(E)\sim e^{\,\mathrm{Const.}\, E^2}$

• URL: http://arxiv.org/abs/2504.06623v1
• Date: Wed, 09 Apr 2025 06:44:28 GMT
• Title: The curious case of operators with spectral density increasing as $Ω(E)\sim e^{\,\mathrm{Const.}\, E^2}$
• Abstract summary: We find that there are indeed such operators, but of a rather unusual types, and for which the wave functions are only barely localized.<n>We point out a tension between such almost delocalized states and black holes as compact objects.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Motivated by a putative model of black holes as quantum objects we consider what types of operators would have a corresponding spectrum. We find that there are indeed such operators, but of a rather unusual types, and for which the wave functions are only barely localized. We point out a tension between such almost delocalized states and black holes as compact objects.

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