Correction To The Radiation Laws Of A Kerr Nonlinear Blackbody

In the early time, Cheng introduced a new kind of blackbody, named a Kerr nonlinear blackbody (KNB), which may have lots of important values of theory and application. Radiation laws, which mainly include Planck radiation law and Stefan-Boltzmann law, are always the most important physical laws of a blackbody, and so in the present thesis we focus our investigation on the correction to the radiation laws of a KNB. The main research results include the following three parts:First, we obtain expressions of the modified radiations laws of a KNB which has finite sizes. Through the use of the semiclassical physics, we get general expressions of the modified Planck and Stefan-Boltzmann blackbody radiation laws as a function of the temperature, size and shape of the cavity. Due to the fact that the expressions above contain some parameters which are diffuicult to be determined, we further investigate two special KNBs, namely a spherical KNB (SKNB) and a rectangular KNB (RKNB), and obtain their explicit expressions of radiation laws, by using of the multi-reflection technique which is another semiclassical theory and different from the former.The case of a KNB with no symmetry axes is also discussed briefly. According to the investigation above, it is found that the modified radiation laws mainly include three terms, i.e. the volume term, the curvature term and the oscillatory term. In addition, we make a numerical calculation of modified radiation laws of a SKNB and a cubic KNB (CKNB) under appropriate conditions. From the caculation, we find the following features:(a) For fixed temperature T, it is found that the dominant term of correction to radiation laws is the oscillatory part, and this term is a decreasing function of the speed of nonpolaritons v(T) and Kerr nonlinear coefficient?. Moreover, we find that the radiant flux density RSK (T) of a KNB is a decreasing function of?and is always larger than Rs (T) of a normal blackbody. The difference of between the two kinds of blackbodies becomes larger with decreasing of parameter, (b) For fixed?, RSK (T) is an increasing function of the temperature T. Furthermore, by comparing a CKNB with a SKNB in several aspects, we consider that a CKNB is more suitable for the experimental verification of corrrction to the radiation laws of a KNB.Second, within the framework of the principle of relativity, we investigate a KNB from the viewpoint of an observer in arbitrary uniform motion with respect to a rest frame of reference of the radiation, and expressions of the modified radiations laws concerned are obtained. It is found that under a special condition the only effect of the motion is to introduce an effective temperature, which replaces the rest-frame temperature of the cavity. Besides, we make an attempt to extend the model of a KNB to the whole Universe and apply the modified radiation laws to 2.7 K cosmic microwave background radiation (CMBR), and so we can explain deviations in the CMBR from the Planck radiation law and what the dark matter is made up of. For the experimental verification, we also investigate the signal S, noise N and signal-to-noise ratio S/N of the radiation of a moving KNB. From this research above, we find that the signal, noise and signal-to-noise ratio of a moving KNB are always larger than those of a normal blackbody, respectively.Third, through the use of Nonextensive statistical mechanics (NSM), and in the limit that q?1, we obtain the asymptotical expressions of the generalized radiation laws of a KNB, which include the Planck radiation law and Stefan-Boltzmann law, in the normalized form. We also make a numerical calculation of the two laws under appropriate conditions. From the calculation, it is found that the bigger q suppresses the radiation in low-frequency region but enhances the radiation in high-frequency. Besides, we also find that the smaller q suppresses the total radiation of a KNB. Finally, we make an attempt to extend the theory of KNB to the whole Universe too.In brief, we consider that the work in this thesis is a development and perfection of the theory of a KNB, and it may lay the foundation for the experimental verification of the model of a KNB.