Finite temperature analysis of quantum Hall-type behavior of charged bosons

The present paper deals with the study of bi-dimensional evolution of complex scalar field in static orthogonal magnetic and electric fields, from both thermodynamic and quantum mechanics points of view. Within a relativistic approach, we derive the quantum eigenstates and the energy spectrum. The expression of the Hall electric field is in good agreement with the experimental data on modulation-doped GaAs film, which have pointed out features that cannot be explained unless one considers quantum effects in Landau levels formation. In the last section, the main thermodynamic quantities of the system are derived, in terms of a physically dimensionless control parameter δ. To leading order in δ ≪ 1, corresponding to the high temperature approximation which is appropriate for classical thermodynamics, we get the bound for the ratio of entropy to energy.