Transport in graphene and statistics of complex systems

• Applicant: Dr. Holger Hennig
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Theoretical Condensed Matter Physics
• Term: from 2011 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 198432750

• Final Report Year: 2014

Final Report Abstract

While the music produced by an ensemble is influenced by multiple factors including musical genre, musician skill, and individual interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction between two humans playing rhythms. We find that the interbeat intervals of both laypeople and professional musicians exhibit scale-free (power law) cross-correlations. Surprisingly, the next beat to be played by one person is dependent on the entire history of the other person's interbeat intervals on time scales up to several minutes. To understand this finding, we propose a general stochastic model for Mutually Interacting Complex Systems (MICS) which suggests a physiologically-motivated explanation for the occurrence of scale-free crosscorrelations. We show that the observed long-term memory phenomenon in rhythmic synchronization can be imitated by `fractal' coupling of separately recorded or synthesized audio tracks. The results can be used to introduce human interactions in audio sequences (e.g., in electronic music), for which a U.S. patent was filed. While this study provides an understanding of fundamental characteristics of timing and synchronization at the inter-brain level, the MICS model may also be applied to study the dynamics of other complex systems where scale-free cross-correlations have been observed, including econophysics, physiological time series, and collective behavior of animal flocks. H. Hennig, R. Fleischmann, T. Geisel. Immer haarscharf daneben. Spektrum der Wissenschaft 9, 16-20 (2012)

Publications

• Global Phase Space of Coherence and Entanglement in a double-well BEC. Phys. Rev. A 86, 051604(R) (2012)
  H. Hennig, D. Witthaut, D.K. Campbell
  
• Musical rhythms: The science of being slightly off. Physics Today 65, 64-65 (2012)
  H. Hennig, R. Fleischmann, T. Geisel
  
• Ballistic versus diffusive transport in graphene. Phys. Rev. B, 88, 125415 (2013)
  M. F. Borunda, H. Hennig, E.J. Heller
  
• Dynamics of entanglement in a dissipative Bose-Hubbard dimer. Phys. Rev. A 88, 063606 (2013)
  T. Pudlik, H. Hennig, D. Witthaut, D.K. Campbell
  (See online at https://doi.org/10.1103/PhysRevA.88.063606)
• Fractal dynamics in chaotic quantum transport. Phys Rev E, 88, 022913 (2013)
  V. Kotimaki, E. Rasanen, H. Hennig, E.J. Heller
  
• Nature of self-localization of Bose-Einstein condensates in optical lattices. Phys. Rev. A 87, 033605 (2013)
  H. Hennig, R. Fleischmann
  (See online at https://doi.org/10.1103/PhysRevA.87.033605)
• Synchronization in human musical rhythms and mutually interacting complex systems. PNAS, September 9, 2014. 111 (36) 12974-12979
  H. Hennig
  (See online at https://doi.org/10.1073/pnas.1324142111)