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A 44-minute talk by Wen Wei Ho at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) explores the concept of geometric quantum drives, with a focus on hyperbolically driven quantum systems. Delivered as part of the Thematic Programme on "Entanglement in Many-body Quantum Matter: Dynamics, Dissipation, Equilibration," this presentation investigates quantum drives beyond the conventional time-periodic (Floquet) and time-quasiperiodic modulations. Discover a theoretical framework where a classical particle moving on a smooth connected manifold steers a quantum Hamiltonian over time, creating diverse time-dependent quantum Hamiltonians whose properties depend on the underlying manifold and trajectory. Learn about "hyperbolically driven quantum systems" applied to compact 2D hyperbolic Riemann surfaces, and understand how they exhibit topologically classified responses in the adiabatic limit that can be measured through simple local observables. Gain insights into this general framework for mapping the landscape of time-dependent quantum systems, investigating their universal phase structures, and potentially enhancing modern quantum simulator capabilities.
