Optimal fiscal policy in a Schumpeterian model

Master'sMASTER OF SOCIAL SCIENCE

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure

Acoustic circular dichroism in a three-dimensional chiral metamaterial

Circular dichroism (CD) is an intriguing chiroptical phenomenon associated with the interaction of chiral structures with circularly polarized lights. Although the CD effect has been extensively studied in optics, it has not yet been demonstrated in acoustic systems. Here, we demonstrate the acoustic CD effect in a three-dimensional chiral metamaterial supporting circularly polarized transverse sound. We find that the effect is negligible in the lossy metamaterial possessing $C_4$ rotational symmetry but can be strongly enhanced in the $C_2$-symmetric system with inhomogeneous loss. The phenomena can be understood based on the properties of the metamaterial's complex band structure and the quality factors of its eigenmodes. We show that the enhanced CD in the $C_2$-symmetric system is attributed to the polarization bandgaps and the non-Hermitian exceptional points appearing near the Brillouin-zone center and boundaries. The results contribute to the understanding of chiral sound-matter interactions and can find applications in acoustic sensing of chiral structures and sound manipulations based on its vector properties.Comment: 9 pages, 9 figure