  We collect and review works which treat two-dimensional electron gases in
quantum wells (mostly GaAs/GaAlAs heterostructures) in the presence of
quantizing magnetic fields as open systems in contact with outside reservoirs.
If a reservoir is sufficiently large, it pins the Fermi level to a certain
energy. As a result, in a varying external magnetic field, the thermodynamic
equilibrium will force oscillations of the electron density in and out of the
quantum well (QW). This leads to a number of physical phenomena in
magneto-transport, interband and intraband magneto-optics, magnetization,
magneto-plasma dispersion, etc. In particular, as first proposed by Baraff and
Tsui, the density oscillations in and out of QW lead to plateaus in the Integer
Quantum Hall Effect (IQHE) at values observed in experiments. The gathered
evidence, especially from magneto-optical investigations, allows us to conclude
that, indeed, in most GaAs/GaAlAs hetrostructures one deals with open systems
in which the electron density in QWs oscillates as the magnetic field varies.
Relation of the density oscillations to other factors, such as electron
localization, and their combined influence on the quantum transport in 2D
electron gases, is discussed. In particular, a validity of the classical
formula for the Hall resistivity {\rho}xy = B/Nec is considered. It is
concluded that the density oscillations are not sufficient to be regarded as
the only source of plateaus in IQHE, although such claims have been sometimes
made in the past and present. Still, our general conclusion is that the
reservoir approach should be included in various descriptions of 2D electron
gases in the present of a magnetic field. An attempt has been made to quote all
the relevant literature on the subject.
