Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Alexander Meyerovich


We report the results of our study of propagation of gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). Our theoretical study is done within the frame of the general theory of transport in systems with random rough boundaries developed by Meyerovich et al. We present a theoretical description of GRANIT experiments in the biased diffusion approximation for waveguides with one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant (O) which determines the depletion times for the gravitational quantum states and the exit neutron count. O is determined by a complicated integral of the correlation function (CF) of surface roughness. For waveguides with 1D roughness most of the calculations can be performed analytically for the main common types of CF. For waveguides with 2D roughness the final calculations are mostly numerical. We also developed useful scaling equations for O which can allow experimentalists to accommodate our results to different experimental setups. The reliable identification of the CF is always hindered by the presence of long fluctuation-driven correlation tails infinite-size samples. In order to deal with this issue, we perform numerical experiments relevant for the identification of the roughness CF. We generate surfaces with predetermined CF using rotation of uncorrelated surfaces or using Monte Carlo simulations based on the Ising model. These numerical experiments show how to circumvent the difficulties that arise in extracting the correlation properties of surface roughness using the data on the surface profile obtained in STM-like experiments. This experience helps us to analyze the new rough mirror and make theoretical predictions for ongoing GRANIT experiments. We also propose an alternative waveguide design which can improve the accuracy of experimental results.