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Dimension Dependent Density-of-States Function and the Radiation Laws
Prabir Kunar Das1, Kamakhya Prasad Ghatak2
1Department of Basic Science and Humanities, Institute of Engineering and Management, Salt Lake, Sector-V, Kolkata 700091, India.
Journal of Nanoscience and Nanotechnology
|December 4, 2018
Summary
Dimension dependent density-of-states (DOS) simplifies derivations of Planck's radiation laws in 1D, 2D, and 3D. This approach also yields Rayleigh-Jeans, Wien's laws, and Stefan-Boltzmann laws across dimensions.
Area of Science:
- Nanoscience and nanotechnology
- Statistical mechanics
- Quantum physics
Background:
- Density-of-states (DOS) is crucial for understanding material properties.
- Classical and quantum physics describe radiation laws with varying dimensional considerations.
Purpose of the Study:
- To demonstrate how dimension dependent density-of-states simplifies radiation law derivations.
- To unify the study of Planck's, Rayleigh-Jeans, Wien's, and Stefan-Boltzmann laws across different dimensions.
Main Methods:
- Utilizing the concept of dimension dependent density-of-states function (DOS).
- Deriving Planck's radiation laws for 3D, 2D, and 1D systems.
- Analyzing the dimensional extremes (Rayleigh-Jeans and Wien's laws).
- Investigating the 3D, 2D, and 1D Stefan-Boltzmann laws.
Main Results:
- A unified and simplified derivation of Planck's radiation laws in 1D, 2D, and 3D.
- Compact derivations for the dimension-dependent extremes: Rayleigh-Jeans and Wien's laws.
- Extension of the study to include 1D, 2D, and 3D Stefan-Boltzmann laws.
Conclusions:
- Dimension dependent DOS provides a powerful and unifying framework for understanding radiation laws.
- The approach offers a more accessible method for deriving and comprehending these fundamental physics laws across various dimensions.
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