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Effective Confining Potential of Quantum States in Disordered Media
Douglas N Arnold1, Guy David2, David Jerison3
1School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Physical Review Letters
|February 20, 2016
Summary
Localized quantum states in disordered systems are governed by an effective potential. This potential explains long-range exponential decay via barrier networks and tunneling, approximating the density of states.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Disordered systems
Background:
- Localized quantum states in random media can show long-range exponential decay.
- Anderson localization describes this phenomenon but lacks a detailed mechanistic explanation for decay.
Purpose of the Study:
- To develop a theory explaining the long-range exponential decay of localized quantum states.
- To introduce an effective potential model for quantum state confinement in disordered systems.
- To connect this model to the density of states in one-dimensional systems.
Main Methods:
- Theoretical modeling of quantum state confinement.
- Analysis of an effective potential governing state boundaries.
- Investigation of multiple tunneling through potential barriers.
- Application of Weyl's formula for density of states approximation.
Main Results:
- An effective potential model is proposed that governs the confinement of localized quantum states.
- The long-range exponential decay is explained by multiple tunneling events within the effective potential's barrier network.
- Weyl's formula, derived from this effective potential, provides a strong approximation for the density of states in various 1D systems.
Conclusions:
- The effective potential model offers a new perspective on Anderson localization and quantum state decay.
- Multiple tunneling through potential barriers is identified as the key mechanism for long-range decay.
- The model's success in approximating the density of states highlights its broad applicability to 1D systems.
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