# Adiabatic Response for Lindblad Dynamics

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## Abstract

We study the adiabatic response of open systems governed by Lindblad evolutions. In such systems, there is an ambiguity in the assignment of observables to fluxes (rates) such as velocities and currents. For the appropriate notion of flux, the formulas for the transport coefficients are simple and explicit and are governed by the parallel transport on the manifold of instantaneous stationary states. Among our results we show that the response coefficients of open systems, whose stationary states are projections, is given by the adiabatic curvature.

## Keywords

Adiabatic response theory Open quantum system Lindblad dynamics Fluxes Currents Principle of virtual work Adiabatic curvature## Notes

### Acknowledgements

J.E.A. is supported by the ISF, the NSF under Grant No. PHY11-25915 and the fund for promotion of research at the Technion. M.F. was supported by UNESCO and ISF. We thank M. Porta for useful discussions.

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