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Quantum Geometry and Bounds on Dissipation in Slowly Driven Quantum Systems
Iliya Esin1,2, Étienne Lantagne-Hurtubise1,3, Frederik Nathan1,4
1California Institute of Technology, Department of Physics and Institute for Quantum Information and Matter, Pasadena, California 91125, USA.
Abstract:
We show that energy dissipation in slowly driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower bounds on dissipation rates in two-tone protocols, such as those employed for topological frequency conversion. Notably, in appropriate limits these bounds are only determined by the topology of the protocol and an effective quality factor of the system-bath coupling. Our results bridge topological and geometric phenomena with energy dissipation in open quantum systems, and further provide design principles for optimal driving protocols.
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