THE CASE FOR DISCRETE ENERGY LEVELS OF A BLACK HOLE

The adiabatic invariant nature of black hole horizon area in a classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which starts from very elementary assumptions, and proceeds by exploiting symmetry. It predicts a uniformly spaced area spectrum for all charges and angular momenta. Area eigenvalues are degenerate; correspondence with black hole entropy then dictates a precise value for the interval between eigenvalues.

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Theoretical Bounds on Electron Energy Filtering in Disordered Nanomaterials

10.26434/chemrxiv.8477168.v1 ◽

2019 ◽

Author(s):

Amro Dodin ◽

Brian F. Aull ◽

Roderick R. Kunz ◽

Adam Willard

Keyword(s):

Theoretical Model ◽

Electron Energy ◽

Energy Levels ◽

Additional Source ◽

Discrete Energy ◽

Energy Filtering ◽

Simple Theoretical Model ◽

Particle Polydispersity ◽

Electron Energy Filtering ◽

Individual Nanoparticles

This manuscript presents a theoretical model for determining the electron energy filtering properties of nanocomposite materials. Individual nanoparticles can serve as energy filters for tunneling electrons due their discretized energy levels. Nanomaterials comprised of many individual nanoparticles can in principle serve the same purpose, however, particle polydispersity can lead to an additional source of energetic broadening. We describe a simple theoretical model that includes the effects of discrete energy levels and inhomogeneous broadening. We use this model to identify the material parameters needed for effective energy filtering by quantum dot solids.

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Small is different

10.1093/oso/9780192846839.003.0007 ◽

2021 ◽

pp. 81-93

Author(s):

Adrian P Sutton

Keyword(s):

Crystal Structure ◽

Electronic Structure ◽

Catalytic Activity ◽

Giant Magnetoresistance ◽

Energy Levels ◽

Exclusion Principle ◽

Thermodynamic Quantities ◽

Discrete Energy ◽

Size Dependent ◽

The World

As the size of a material decreases to the nanoscale its properties become size-dependent. This is the world of nanoscience and nanotechnology. At the nanoscale the crystal structure may change and thermodynamic quantities such as the melting point also change. Changes in the catalytic activity and colour of nanoparticles suspended in a liquid indicate changes to the electronic structure. Quantum dots have discrete energy levels that can be modelled with the particle-in-a-box model. Excitons may be created in them using optical illumination, and their decay leads to fluorescence with distinct colours. The classical and quantum origins of magnetism are discussed. The origin of magnetoresistance in a ferromagnet is described and related to the exclusion principle. The origin of the giant magnetoresistance effect and its exploitation in nanotechnology is outlined.

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PARTICLE NATURE OF LIGHT – DISCRETE ENERGY LEVELS

Laser Fundamentals ◽

10.1017/cbo9780511616426.005 ◽

2004 ◽

pp. 45-88

Keyword(s):

Energy Levels ◽

Discrete Energy ◽

Particle Nature

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Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields II

Nagoya Mathematical Journal ◽

10.1017/s0027763000006115 ◽

1997 ◽

Vol 145 ◽

pp. 69-98

Author(s):

Tetsuya Hattori

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Discrete Spectrum ◽

Bound States ◽

Atomic System ◽

Energy Levels ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

Many Body ◽

Discrete Energy

This paper is continuation from [10], in which we studied the discrete spectrum of atomic Hamiltonians with non-constant magnetic fields and, more precisely, we showed that any atomic system has only finitely many bound states, corresponding to the discrete energy levels, in a suitable magnetic field. In this paper we show another phenomenon in non-constant magnetic fields that any atomic system has infinitely many bound states in a suitable magnetic field.

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