INVESTIGATIONS OF THE RECOVERY OF THE PHONON DENSITY OF STATES FROM SPECIFIC-HEAT - NUMERICAL STUDY

An iterative algorithm for the determination of the phonon density of states (DOS) from the specific heat is presented based on the general theory of the amplitude-phase retrieval problem. From the model calculation, it is found that a convergent solution can always be obtained. However, the profile of the recovered DOS depends on the initial frequency distribution used in the algorithm since the inverse problem is inherently ill-posed. In order to obtain the ideal reconstruction of the DOS, it is necessary to introduce additional information about the character of the DOS to guide the choice of the initial distribution. The algorithm can also give a robust reconstruction of the DOS from specific heat data contaminated with random noise. The recovery of the DOS based on specific heat data in a confined temperature range has also been examined in detail.