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How the site degree influences quantum probability on inhomogeneous substrates
A M C Souza1, R F S Andrade2, N A M Araújo3,4
1Departamento de Física, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, Brazil.
Physical Review. E
|May 17, 2017
Summary
The quantum probability of finding an electron on a site depends on its connectivity (degree). For bipartite lattices, this probability is independent of energy, but for other structures, it varies with energy and degree.
Area of Science:
- Condensed Matter Physics
- Network Science
- Quantum Mechanics
Background:
- Understanding electron behavior in diverse structures is crucial.
- Node degree significantly influences network properties.
- Quantum wave functions are fundamental to electronic behavior.
Purpose of the Study:
- To investigate how node degree and energy affect electronic wave functions.
- To analyze quantum probability distribution across different network structures.
- To determine the relationship between site connectivity and quantum probability.
Main Methods:
- Analytical derivation for bipartite lattices.
- Exact evaluation for a 1D semiregular lattice.
- Numerical simulations for percolation clusters and complex networks.
Main Results:
- For bipartite lattices, quantum probability (P_k(E)) is independent of energy (E≠0) and depends only on node degree (k).
- For nonbipartite structures, P_k(E) can depend on E, showing larger probabilities for small E and small k.
- Maximum probability values shift to higher |E| as k increases in semiregular lattices.
Conclusions:
- The energy independence of quantum probability on node degree holds for bipartite lattices.
- A general trend suggests energy-dependent quantum probability in complex networks, influenced by node degree.
- Findings provide insights into electron localization in disordered and complex systems.
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