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Harding Distinguished Postgraduate Scholars Programme


  Javier Echevarría Cuesta,


  Pure Mathematics and Mathematical Statistics, Darwin College

  PhD thesis: Emergence of quantum dynamics from chaos.

  Research interests:
  1. Hyperbolic geometry.
  2. Quantum chaos.
                                3. Microlocal analysis.
                                4. Dynamical systems.

My PhD focuses on the relationship between chaotic dynamical systems and quantum mechanics. The usual setting where this connection comes up is in hyperbolic geometry. 

Thanks to results such as Egorov’s theorem in semiclassical analysis, it is by now well know that classical dynamics emerge in the high frequency limit of quantum dynamics. However, one of the surprising interpretations of recent advances in dynamical systems is that the opposite direction can also be true: quantum dynamics emerge from classical dynamics when the latter are chaotic. For instance, in the special case of the geodesic flow on a surface of constant negative curvature, the transfer operator has a dominant quantum component which has the same spectrum as the wave operator. We thus recover the dynamics of a quantum free particle. Beyond its intrinsic physical interest, this interpretation raises a lot of questions from the mathematical point of view.

Who or what inspired you to pursue your research interests?
I was inspired to pursue my research interests while attending a conference in Porquerolles, France. At the end of a presentation, one of the participants (with whom I later got to work with) suggested under his breath that perhaps the probabilistic aspect of quantum mechanics could be explained away with chaos theory. He was aware that ushering such a claim was very bold: the scientific and philosophical ramifications would be tremendous. I was immediately fascinated by the idea.