Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct an ensemble of maps from a given complex network to a circle S1, such that closely related nodes on the network are grouped into sharply concentrated clusters on S1. The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster "orbitals" in an effective tight-binding model recapitulating the network. python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics