Microwave studies of the Gaussian symplectic and the chiral ensembles

• Applicant: Professor Dr. Hans-Jürgen Stöckmann
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 260221821

The universal properties of the spectra of chaotic systems, e.g. the spacing distribution of neighboring eigenvalues, coincide with those of random matrix ensembles with corresponding symmetries. This universality is the essence of the meanwhile proven conjecture of Bohigas, Giannoni, Schmit. Systems with time-reversal symmetry (TRS) and no spin 1/2 are described by the Gaussian orthogonal ensemble (GOE), those with spin 1/2 by the symplectic (GSE), and those with broken TRS by the unitary (GUE) ensemble.There is an abundant number of experimental realizations for the GOE and a small number for the GUE. For the GSE the first experimental realization after 50 years of random matrix theory (RMT) had been achieved by us in the present project in a microwave graph, a network with peculiar symmetries mimicking a spin 1/2 system.In the continuation of this project we plan to study the scattering properties of GSE graphs. Apart from a first experiment in our group described in this application, this is a completely new field of research. Also RMT, well established for the GOE and the GUE, still has to be developed in mayor parts for the GSE.For systems with particle-antiparticle symmetries three new random matrix ensembles appear, the chiral GOE, GUE, GSE, respectively. In our first application we proposed to realize the chiral GOE in a microwave equivalent of graphene set up by dielectric cylinders. For reasons described in the application we decided to change to a much simpler system, which already exhibits chiral symmetry, the linear chain.The ongoing experiments already demonstrate that we had been successful in the realization of the chiral GOE. In the prolongation we plan to extend the studies to the chiral GUE and the chiral GSE. The main objective of this project including its prolongation is the first experimental realization of four of the ten random matrix ensembles.By means of a combination of an externally driven diode with a T junction non-stationary graphs may be generated. Using periodic time dependencies in a GSE graph we plan to realize a microwave equivalent of spin resonance. Even an equivalent of spin relaxation can be established by applying in addition a stochastically varying time-dependence. This would open a new access to the test of spin relaxation theories.

• DFG Programme: Research Grants
• International Connection: China, France
• Co-Investigator: Professor Dr. Ulrich Kuhl
• Cooperation Partner: Privatdozentin Dr. Barbara Dietz