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In this paper, we prove that for any $d$-frequency analytic quasiperiodicSchr\"odinger operator, if the frequency is weak Liouvillean, and the potentialis small enough, then the corresponding operator has absolutely continuousspectrum. Moreover, in the case $d=2$, we even establish the existence of acspectrum under small potential and some super-Liouvillean frequency, and thisresult is optimal due to a recent counterexample of Avila and Jitomirskaya.

Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schr\"odinger operator