  We investigate the orbital Hall effect through a mesoscopic device with
momentum-space orbital texture that is connected to four semi-infinite
terminals embedded in the Landauer-B\"uttiker configuration for quantum
transport. We present analytical and numerical evidence that the orbital Hall
current exhibits mesoscopic fluctuations, which can be interpreted in the
framework of random matrix theory (RMT) (as with spin Hall current
fluctuations). The mesoscopic fluctuations of orbital Hall current display two
different amplitudes of 0.36 and 0.18 for weak and strong spin-orbit coupling,
respectively. The amplitudes are obtained by analytical calculation via RMT and
are supported by numerical calculations based on the tight-binding model.
Furthermore, the orbital Hall current fluctuations lead to two relationships
between the orbital Hall angle and conductivity. Finally, we confront the two
relations with experimental data of the orbital Hall angle, which shows good
concordance between theory and experiment.
