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Universality at Breakdown of Quantum Transport on Complex Networks
Nikolaj Kulvelis1, Maxim Dolgushev1, Oliver Mülken1
1Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.
Physical Review Letters
|October 3, 2015
Summary
We found that quantum transport efficiency in treelike networks transitions from efficient to inefficient based on node functionality. This transition is characterized by a universal exponent in the infinite system size limit.
Area of Science:
- Quantum physics
- Complex networks
- Statistical mechanics
Background:
- Understanding quantum transport in complex systems is crucial.
- Network structure significantly impacts transport properties.
- Quantifying global transport efficiency requires robust measures.
Purpose of the Study:
- To derive bounds for global quantum transport efficiency on complex networks.
- To investigate the transition from efficient to inefficient transport in treelike networks.
- To identify universal characteristics of this transition.
Main Methods:
- Analysis of the Hamiltonian spectrum for quantum transport.
- Derivation of bounds for time-averaged return probability.
- Analytical solutions for treelike, deterministic, and fractal networks.
- Monte Carlo simulations for scale-free trees.
Main Results:
- Established bounds for global transport efficiency.
- Identified a critical transition in treelike networks dependent on node functionality.
- Characterized the transition with a universal exponent in the infinite system size limit.
- Confirmed findings with specific network models and simulations.
Conclusions:
- Node functionality critically determines quantum transport efficiency in treelike networks.
- The observed transition is a universal phenomenon in such systems.
- The study provides a theoretical framework for understanding quantum transport in complex network architectures.
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