Quantum derivatives and high-frequency gain in semiconductor superlattices

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We derive simple difference formulas describing a small-signal absorption of THz field in a semiconductor superlattice driven by a microwave pump. We give a transparent geometric interpretation of these formulas that allows a search of optimum conditions for the gain employing only a simple qualitative analysis. Our theoretical approach provides a powerful tool for finding the correspondence between quasistatic and dynamic regimes in ac-driven semiconductor superlattices.
Submitted to proceedings of 4th Int. Symp. Nanostructures: Physics and Technology (St Petersburg, Russia, June 26-30, 2006). For detailed consideration see in cond-mat/0602209

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