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Physics and Astronomy
Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search for SPT physics in non-interacting bosonic systems, calling for a much needed paradigm shift beyond equilibrium.
The research program undertaken in this thesis provides a systematic investigation of effective non-Hermiticity in non-interacting bosonic Hamiltonians and establishes the extent to which one must move beyond equilibrium to uncover SPT-like bosonic physics. Beginning in the closed-system setting, whereby systems are modeled by quadratic Hamiltonians, we classify the types of dynamical instabilities effective non-Hermiticity engenders. While these flavors of instability are distinguished by the algebraic behavior of normal modes, they can be unified under the umbrella of spontaneous generalized parity-time symmetry-breaking. By harnessing tools from Krein stability theory, a numerical indicator of dynamical stability phase transitions is also introduced. Throughout, the role played by non-Hermiticity in dynamically stable systems is scrutinized, resulting in the discovery of a Hermiticity-restoring duality transformation.
Building on the preceding analysis, we take the necessary plunge into open bosonic systems undergoing Markovian dissipation, modeled by quadratic (Gaussian) Lindblad master equations. The first finding is that of a uniquely-bosonic notion of dynamical metastability, whereby asymptotically stable dynamics are preempted by a regime of transient amplification. Incorporating non-trivial topological invariants leads to the notion of topological metastability which, remarkably, features tight bosonic analogues to the edge modes characteristic of fermionic SPT phases - which we deem Majorana and Dirac bosons - along with a manifold of long-lived quasi-steady states. Implications regarding the breakdown of Noether's theorem are explored, and several observable signatures based on two-time correlation functions and power spectra are proposed.
Flynn, Vincent Paul, "Effective Non-Hermiticity and Topology in Markovian Quadratic Bosonic Dynamics" (2023). Dartmouth College Ph.D Dissertations. 142.
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