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"The dephasing between the Bragg pulses is not unitary, I believe it can be explicitly written in Lindblad form and generates heat. I believe this Point of view is the same as (among others) the papers of Allahverdyan and Van Nieuwenhuizen cited, but I don't know how far it applies to your work."

The context for this comment is that a density matrix that is not diagonal in the energy basis undergoes decoherence and the off diagonal terms go to zero. Can this type of decoherence be associated with the generation of heat? How does one define heat in such a context?

Any references will be also be much appreciated.