Radiation spectrum and the thermodynamics of quantum cubic cavities

In this paper, the density of modes in quantum cubic cavities is calculated taking into account the small number of modes. Then the `spatial quantization' fluctuations, which appear as a correction factor in the mode density, are introduced in the Planck law. The discrete form of the Planck radiation spectrum is demonstrated and the limits of this double-quantum regime of the cubic cavity are set for the product of cavity size by temperature. LT(epsilon) (0.1, 1). A reciprocity rule for the cavity size and the temperature is shown. Calculating the total energy in the quantum cubic cavities (QCC), we found out a `corrected' Stefan-Boltzmann law for the double-quantum regime. Furthermore, the corrections for all thermodynamic functions of the photon gas in QCC are given.