Lessons from an Emergent Phenomenon: Vortex Dynamics in Super Media

1. Lessons from an Emergent Phenomenon: Vortex Dynamics in Super Media Ping Ao Department of Mechanical Engineering and Department of Physics Washington University May 14-17, 2007, Complexity Conference, Urbana, USA Its history is a vortex or hurricane! P. Ao, cond-mat/0610753, http://arxiv.org/PS_cache/cond-mat/pdf/0610/0610753.pdf Other complexity related works: Evolution: Ao, Physics of Life Reviews, 2005 Phage lambda genetics switch: Zhu et al, Functional and Integrative Genomics 2004; chapter in Introduction to Systems Bioloyg, 2007 Evolution and development: Ao, Biological Theory, 2007 Complex adaptive landscape: Ao, Kwon, Qian, Complexity, 2007

2. Connection to Complexity ~ 1023 parts Reduced dynamics: BCS theory (uiuc theory) Further reduction: (Eric J., Dale van H., this conference) Three main features of self-organization for complexity (Schuster, Complexity, 2007): (i) structure ? quantized vortex (ii) Function ? equation of motion (iii) intention or seeming purpose ? ??

3. Structure ? Quantized Vortex L. Landau didn�t want it in his theory of Helium II (~ 1940): stability concern. Landau criterion: no boundary, no topology F. London (1948), L. Onsager (1949) argued for its existence in superconductors and superfluids, respectively. R. Feynman extended Onsager�s idea (1954) A. Abrikosov�s vortex lattice (1955) 20 years later it was established: J. Vinen, Fairbank, C.N. Yang, � (~1960) Macroscopic quantum phenomena, More Nobel Prizes??

4. Function ? Equation of Motion Phase slippage----Josephson-Anderson effect Equation of motion for vortex dynamics: The pseudo debate between Bardeen and Stephen etc on one side, and Vinen, de Genes etc on other side The quarrel between Landau school and a loose collection associated with Seattle The real issue to understand the Hall anomaly The use and misuse of relaxation time approximation

5. Landau vs Seattle The main difference: Landau school (1970�s � now ??): Practically zero transverse force (the Magnus force) on a moving vortex in superconductors. Seattle �school� (1990�s � now ): Practically same transverse force (the Magnus force) on a moving vortex in superconductor for clean and dirty superconductors, guaranteed by Anderson�s dirty superconductor theorem.

6. What Happens Experimentally? Hall anomaly: well established since 1970�s Not understandable by a single, independent vortex dynamics type models Direct measurement: not until 1997!

7. More on Swedish Experiment Three similarities to J. Vinen�s experiment on single vortex in helium II in in 1961: Directly measuring the force Highly controversial Conceptually simple

8. Equation of Motion

9. Derivation from BCS TheoryAo and Zhu, Phys. Rev. B, 1999

13. Explaining Hall Anomaly Vortex many-body effect: Vacancies or Vacancies-like excitations in Abrikosov vortex lattice vs Interstitials or Interstitials-like excitations Ao, J. Supercond. 1995; J.Phys. Conden. Matt. 1998. Emergent phenomena built upon emergent phenomena----hierarchical structure

14. Subtle Mistake in the Approach of Landau School Two kinds of linear response theories (Mis)use of relaxation time approximation

15. Back to Complexity and Emergence Two of three main features of self-organization for complexity can be nicely illustrated by vortex dynamics: (i) New structure ? quantized vortex (ii) Novel function ? equation of motion (iii) Intention or seeming purpose ? ??

16. Lessons One of all time beautiful examples of physical theories motivated by logical consistency is Dirac`s theory of relativistic quantum electrodynamics: The void in the filled Fermi sea led Dirac to predict a new particle, later called positron. The influence of its success is now on all branches of modern physics. Another beautiful example is Abrikosov`s vortex lattice theory, inferred as a very natural consequence, in the hindsight, of the Ginzburg-Landau theory. Beautiful and profound theories can also be obtained by careful consideration and critical analysis of experimental data, the opposite methodology. One of such all time examples is the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Again, its influence is now on all branches of modern physics.

17. Daily theoretical physicists` activities are usually between those two extremes. For example, by combining limited experimental data with theoretical insights, difficult aspects of the vortex dynamics puzzle were solved by Nozieres and Vinen and by Bardeen and Stephen in the 1960`s. Is there a take-home rule on how to successfully use those two opposite methodologies? The fun an challenge of practicing theoretical research, as well as its pitfall, are that there is no ready formula for the right mix of two extremes. You can only find it out by getting your hands wet and dirty, preferably at the spot where the water is the roughest.

18. Very Active Topic Many phenomena are counter-intuitive. P. Goldbart (this conference) D.J. Thouless and J.R. Anglin, cond-mat/0703523 Thank you very much for your attention.