Duality of bounded and scattering wave systems with local symmetries

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard wall boundaries leads to extrema of the eigenenergies. The underlying wavefunction becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated at hand of a numerical example with a potential consisting of two domains of local symmetry, each one comprised of Dirac ? barriers.Comment: 8 pages, 6 figure

Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain

We show that it is possible to successfully, rapidly, and robustly transfer a topological vibrational edge mode across a time-varying mechanical chain. The stiffness values of the springs of the chain are arranged in an alternating staggered way such that we obtain a mechanical analog of the quantum Su-Schrieffer-Heeger model, which exhibits a nontrivial topological phase. Using optimal control methods, we are able to design control schemes for driving the stiffness parameters such that the transfer is done with high fidelity, speed, and robustness against disorder as well as energy amplification of the target edge mode. © 2020 American Physical Society

Fast, robust and amplified transfer of topological edge modes on time-varying mechanical chain

We show that it is possible to successfully, rapidly and robustly transfer a topological vibrational edge mode across a time-varying mechanical chain. The stiffness values of the springs of the chain are arranged in an alternating staggered way, such that we obtain a mechanical analog of the quantum Su-Schrieffer-Heeger model which exhibits a non trivial topological phase. Using optimal control methods, we are able to design control schemes for driving the stiffness parameters, such that the transfer is done with high fidelity, speed and robustness against disorder as well as energy amplification of the target edge mode.Comment: 10 pages, 9 figure

Duality of bounded and scattering wave systems with local symmetries

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domainwise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard-wall boundaries leads to extrema of the eigenenergies. The underlying wave function becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated through a numerical example with a potential consisting of two domains of local symmetry, each comprised of Dirac δ barriers. © 2019 American Physical Society