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High-harmonic generation (HHG) has been established as a powerful tool for studying structure and dynamics of quantum systems in gas and solid phases. To date, only a few studies have extended HHG spectroscopy to liquids, and much remains unresolved concerning the information that can be extracted from HHG spectra about the local liquid environment and the potential of HHG as a nonlinear probe of solvation dynamics. In this work, we investigate HHG in liquid binary solutions consisting of mixtures of aromatic benzene derivatives solvated in methanol. We observe evidence of a localized solvation structure that is imprinted on the harmonic spectra in the form of a strongly suppressed harmonic order, and an overall reduction of the total harmonic yield. We characterize this behavior as a function of laser parameters, concentration, and other halogenated benzene derivatives in methanol solution. Guided by theory, we interpret the results in terms of a localized solvation shell that is formed in specific solutions and acts like a local scattering barrier in the HHG process. This work demonstrates the potential of high-harmonic spectroscopy in liquids to extract detailed information about the structure and dynamics of solvation while expanding our understanding of the fundamental mechanism of HHG in systems with short-range order. 

Abstract We provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates. The more general expression, in which the iterate is a linear combination of a Hardy field function of polynomial growth and a tempered function, is studied as well. 

Abstract We establish sufficient and necessary conditions for the joint transitivity of linear iterates in a minimal topological dynamical system with commuting transformations. This result provides the first topological analogue of the classical Berend and Bergelson joint ergodicity criterion in measure-preserving systems.