SAX J2103.5+4545 is the Be/X-ray binary with the shortest orbital period.
It shows extended bright and faint X-ray states that last for a few hundred
days. The main objective of this work is to investigate the relationship
between the X-ray and optical variability and to characterise the spectral
and timing properties of the bright and faint states. We have found a
correlation between the spectral and temporal parameters that fit the
energy and power spectra. Softer energy spectra correspond to softer power
spectra. That is to say, when the energy spectrum is soft the power at high
frequencies is suppressed. We also present the results of our monitoring of
the Halpha line of the optical counterpart since its discovery in 2003.
There is a correlation between the strength and shape of the Halpha line,
originated in the circumstellar envelope of the massive companion and the
X-ray emission from the vicinity of the neutron star. Halpha emission,
indicative of an equatorial disc around the B-type star, is detected
whenever the source is bright in X-rays. When the disc is absent, the X-ray
emission decreases significantly. The long-term variability of
SAX J2103.5+4545 is characterised by fast episodes of disc loss and
subsequent reformation. The time scales for the loss and reformation
of the disc (about 2 years) are the fastest among Be/X-ray binaries.