Aims. We have searched for temporal variations of narrow absorption lines in high resolution quasar spectra. A sample of 5 distant sources have been assembled, for which 2 spectra - VLT/UVES or Keck/HIRES - taken several years apart are available. Methods. We first investigate under which conditions variations in absorption line profiles can be detected reliably from high resolution spectra, and discuss the implications of changes in terms of small-scale structure within the intervening gas or intrinsic origin. The targets selected allow us to investigate the time behavior of a broad variety of absorption line systems, sampling diverse environments: the vicinity of active nuclei, galaxy halos, molecular-rich galaxy disks associated with damped Lya systems, as well as neutral gas within our own Galaxy. Results. Absorption lines from MgII, FeII or proxy species with lines of lower opacity tracing the same kind of gas appear to be remarkably stable (1 sigma upper limits as low as 10 % for some components on scales in the range 10 - 100 au), even for systems at z_abs ~ z_e. Marginal variations are observed for MgII lines toward PKS 1229-021 at z_abs = 0.83032; however, we detect no systems displaying changes as large as those reported in low resolution SDSS spectra. In neutral or diffuse molecular media, clear changes are seen for Galactic NaI lines toward PKS 1229-02 (decrease of N by a factor of four for one of the five components over 9.7 yr), corresponding to structure at a scale of about 35 au, in good agreement with known properties of the Galactic interstellar medium. Tentative variations are detected for H2 J=3 lines toward FBQS J2340-0053 at z_abs =2.05454 (~35% change in column density), suggesting the existence of structure at the 10 au-scale for this warm gas. A marginal change is also seen in CI from another velocity component (~70% variation in N(CI)).
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