  Development of fundamental physics relies on the constancy of various
fundamental quantities such as the fine structure constant. Detecting or
constraining the possible time variations of these fundamental physical
quantities is an important step toward a complete understanding of basic
physics. Here we present the results from a detailed many-multiplet analysis
performed using high signal-to-noise ratio, high spectral resolution
observations of 23 Mg II systems detected toward 18 QSOs in the redshift range
0.4<z<2.3 obtained using UVES at the VLT. We validate our procedure and define
the selection criteria that will avoid possible systematics using detail
analysis of simulated data set. We show our Voigt profile fitting code recovers
the variation in \alpha very accurately when we use single component systems
and multiple component systems that are not heavily blended. Spurious
detections are frequently seen when we use heavily blended systems or the
systems with very weak lines. Thus we avoided heavily blended systems and the
systems with Fe II column density < 2x10^12 cm^-2 in the analysis. All steps
involved in the analysis are presented in detail. The weighted mean value of
the variation in \alpha obtained from our analysis over the redshift range
0.4<z<2.3 is {\Delta\alpha/\alpha} = (-0.06+/-0.06)x10^-5. The median redshift
of our sample is 1.55 the 3\sigma upper limit on the time variation of $\alpha$
is -2.5x10^-16 yr^-1< (\Delta\alpha/\alpha\Delta t) <+1.2x10^-16 yr^-1. To our
knowledge this is the strongest constraint from quasar absorption line studies
till date.
