Mikrowellenuntersuchungen des Gauß'schen symplektischen und der chiralen Ensembles
Zusammenfassung der Projektergebnisse
Random matrix theory has proven extremely successful in the description of the statistical properties of the spectra of chaotic systems. Depending on the presence and absence of time-reversal symmetry and/or a spin 1/2 there are three random matrix ensembles. For the orthogonal one there is an abundant number of experimental realizations, one of them achieved in a pioneering microwave experiment in the group of the applicant. For the unitary ensemble the number of systematic studies is small, again one of them by us. Object of the preceding DFG project was the first random matrix study of the symplectic ensemble in a microwave network mimicking a spin 1/2, fifty years after the invention of random matrix theory. Main object of the present DFG project was a microwave realization of the chiral ensembles. A chiral symmetry is found, e. g. in the Dirac equation, but for the realization relativistic electrons are not needed. Sufficient is a system consisting of two subsystems I and II with interactions only between I and II, but no internal interactions within I or II. This was realized by us by a linear chain of evanescently coupled dielectric cylinders. For seven of the altogether ten random matrix ensembles there are now microwave realizations, for the symplectic ensemble and the three chiral ensembles exclusively by us. This demonstrates the high versatility of the microwave techniques. They allow in particular for a straightforward rearrangement of the geometry needed for ensemble averages, an approach hardly possible for any other method. The whole spin 1/2 physics has now become accessible to microwave analogue studies meaning a huge potential for future works. There is already a publication on the transport properties through microwave graphs with orthogonal, unitary, and symplectic symmetry. In the present project we continued in this direction with a study of the fluctuation properties of the transport through graphs with a symplectic symmetry. Another intriguing aspect is the option to simulate NMR in a microwave network. To this end one has to change bond lengths within the network with frequencies of 10 to 50 MHz. This is achieved by means of variable capacity diodes. In a preliminary step we succeeded already in a microwave realization of the motional narrowing phenomenon, on its own a subject of interest in NMR physics. All essential ingredients for the realization of an NMR analogue have thus been successfully tested, but the last step still has to be done.
Projektbezogene Publikationen (Auswahl)
- Microwave Realization of the Gaussian Symplectic Ensemble, Phys. Rev. Lett. 117, 064101 (2016)
A. Rehemanjiang et al.
(Siehe online unter https://doi.org/10.1103/PhysRevLett.117.064101) - A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles, Phys. Rev. Lett., 124, 116801 (2020)
A. Rehemanjiang et al.
(Siehe online unter https://doi.org/10.1103/PhysRevLett.124.116801)
