QUANTUM TRANSPORT EQUATION FOR SYSTEMS WITH ROUGH SURFACES AND ITS APPLICATION TO ULTRACOLD NEUTRONS IN A QUANTIZING GRAVITY FIELD
Escobar M., Meyerovich A.E.

Поступила в редакцию: 7 Мая 2014

DOI: 10.7868/S0044451014120141

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We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide. Contribution for the JETP special issue in honor of A. F. Andreev's 75th birthday}