9 research outputs found
Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry
The Landauer-B\"uttiker formalism establishes an equivalence between the
electrical conduction through a device, e.g., a quantum dot, and the
transmission. Guided by this analogy we perform transmission measurements
through three-port microwave graphs with orthogonal, unitary, and symplectic
symmetry thus mimicking three-terminal voltage drop devices. One of the ports
is placed as input and a second one as output, while a third port is used as a
probe. Analytical predictions show good agreement with the measurements in the
presence of orthogonal and unitary symmetries, provided that the absorption and
the influence of the coupling port are taken into account. The symplectic
symmetry is realized in specifically designed graphs mimicking spin 1/2
systems. Again a good agreement between experiment and theory is found. For the
symplectic case the results are marginally sensitive to absorption and coupling
strength of the port, in contrast to the orthogonal and unitary case.Comment: 6 pages, 6 figure
Microwave Studies of Three Chiral Ensembles in Chains of Coupled Dielectric Resonators
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian orthogonal, Gaussian unitary, and Gaussian symplectic one. With a further particle-antiparticle symmetry the chiral variants of these ensembles, the chiral orthogonal, unitary, and symplectic ensembles (the BDI, AIII, and CII in Cartanâs notation) appear which are the main point of interest in this paper. Following a recently published work on chiral random matrix ensembles and their experimental realizations, Phys. Rev. Lett.124, 116801 (2020), this is achieved by using dielectric cylinders placed between two parallel aluminium plates. These cylinders act as microwave resonators which are used to create tight-binding chains of finite length up to N = 5. The different ensembles are achieved by using different types of couplings: (i) for the orthogonal case spatial proximity is used, for the unitary case microwave circulators are used, and (ii) for the symplectic case a combination of circulators and cables is used to create the necessary symmetry. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero are verified by a comparison with theory taking the finite size of the systems into account. We will show that the difference to the expected universal behavior is given by logarithmic corrections only. These corrections stem from the Hamiltonians having zero entries in their off-diagonal blocks
Microwave Realization of the Chiral Orthogonal, Unitary, and Symplectic Ensembles
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian orthogonal (GOE), Gaussian unitary (GUE), and Gaussian symplectic (GSE) one. With a further particle-antiparticle symmetry the chiral variants of these ensembles, the chiral orthogonal, unitary, and symplectic ensembles (the BDI, AIII, and CII in Cartanâs notation) appear. We exhibit a microwave setup based on a linear chain of evanescently coupled dielectric cylindrical resonators allowing us to study all three chiral ensembles experimentally. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero could be verified
Microwave Realization of the Gaussian Symplectic Ensemble
This work was funded by the Deutsche Forschungsgemeinschaft via the individual Grants No. STO 157/16-1 and No. KU 1525/3-1. C.âH.âJ. acknowledges the Leverhulme Trust (Grant No. ECF-2014-448) for financial support