High harmonic generation (HHG) from gases and solids has been studied extensively. Whereas for liquids, it is far more challenging to understand the ultrafast dynamics with conventional methods. From a statistical perspective, we investigate the liquid-phase HHG theoretically by using a disordered linear chain. Our results reveal that (i) the harmonic spectra are characterized by a transition energy that separates the spectra into a low-energy region containing only odd harmonics and a high-energy region containing both even and odd harmonics with low yields; (ii) the transition energy depends on the fluctuation of structure and the field strength, but independent of the laser wavelength; (iii) the occurrence of dephasing is a natural result of the electron dynamics modulated by the long-range disorder. Furthermore, a simple formula is proposed to identify the transition energy, from which we correctly reproduce the experimental cutoff energies of HHG from liquid ethanol. Our results pave the way to better understand and control the HHG in liquids as another compact HHG source.
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