The curious case of operators with spectral density increasing as Ω(E)∼ e ^{Const. E2}

2025/04/09 by Erik Aurell, Satya N. Majumdar, Aurell, Erik +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Numerical methods in inverse problems #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2504.06623

openalex publication_date 2025/04/09 · openalex created_date 2025/10/02 · openalex updated_date 2026/07/30

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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