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

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.

arXiv commentAPS format, 5 pages, 50 references, no figures

References in corpus (37)

• The World as a Hologram
• Quasinormal modes of black holes and black branes
• The holographic principle
• Quasinormal modes of black holes: from astrophysics to string theory
• Quantum Geometry and Black Hole Entropy
• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• D-brane Approach to Black Hole Quantum Mechanics
• The entropy of Hawking radiation
• Black hole entropy in Loop Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• Jerusalem Lectures on Black Holes and Quantum Information
• Hawking Radiation and Black Hole Thermodynamics
• Spectroscopy of the quantum black hole
• The physical interpretation of the spectrum of black hole quasinormal modes
• A Dynamical Approach to Temperature
• The fuzzball proposal for black holes
• D-branes and Fat Black Holes
• The Black Hole information problem: past, present, and future
• Pseudospectrum and black hole quasi-normal mode (in)stability
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Conservative solutions to the black hole information problem
• On the dispute between Boltzmann and Gibbs entropy
• Negative temperatures and the definition of entropy
• Non-Thermal Corrections to Hawking Radiation Versus the Information Paradox
• Level Density of a Bose Gas and Extreme Value Statistics
• Structure of the Spherical Black Hole Interior
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• On the Quantum Density of States and Partitioning an Integer
• A proposal to resolve the black hole information paradox
• Integer Partitions and Exclusion Statistics
• Overcounting of interior excitations: A resolution to the bags of gold paradox in AdS
• Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams
• Black Holes and Marchenko-Pastur Distribution
• The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon
• Many-body density of states of bosonic and fermionic gases: a combinatorial approach
• Boltzmann Distribution on "Short" Integer Partitions with Power Parts: Limit Laws and Sampling