Exploring non-Hermitian physics in mechanical metamaterials

Martello, Enrico ORCID: 0000-0002-9041-4949 (2023). Exploring non-Hermitian physics in mechanical metamaterials. University of Birmingham. Ph.D.

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Abstract

One of the postulates of quantum mechanics demands observables to be real, and as a consequence Hamiltonians, representing the energy of a system, to be Hermitian. In fact, this constraint is unnecessarily strong, since also a non-Hermitian Hamiltonian can feature a real spectrum, for example, in the case that they satisfy e.g. both parity and time-reversal (PT) symmetries, as obtained by Bender and Boettcher in 1998. Following the wave of interest towards this topic in the last decades, I will review the consequences of lifting the Hermiticity condition for Hamiltonians described by time-dependent parameters. I will use this to investigate effects related to the adiabatic geometric phase in PT-symmetric non-Hermitian systems. This will be investigated both theoretically, and with our experimental collaborators, in a non-Hermitian dimer model realized by a mechanical metamaterial platform. Metamaterials consist of an arrangement of “meta-atoms”, artificially designed units, in this case corresponding to classical harmonic oscillators, whose interactions are then engineered in order to obtain the desired effective Hamiltonian. We will exploit the controllability of this platform to investigate not only the non-Hermitian geometric phase, but then to study the dynamic properties of the interacting so-called Hatano-Nelson dimer, where the interplay of non-Hermiticity and interactions leads to the co-existence of stable and unstable population dynamics. This sets the ground for the final part of this thesis, in which I will theoretically investigate a larger system with three sites with periodic boundary conditions: a triangular plaquette, pierced by a magnetic flux, that might in turn be of interest for the investigation of topological phenomena in the future.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):