NUMERICAL AND THEORETICAL STUDY OF THE CASIMIR FORCE CORRECTIONS BETWEEN TWO ROUGH SURFACES

The Casimir force between two rough surfaces grown through statistical growth models is studied, both theoretically and numerically. The models include the random deposition (RD), the random deposition with surface relaxation (RDSR), and the restricted solid-on-solid growth (RSOS). To calculate the Casimir force, the pairwise summation (PWS) method in [Formula: see text] dimensions is used. First, the force between two growing surfaces with RD equations, Edwards–Wilkinson, (EW) and Kardar–Parisi–Zhang (KPZ) equations is theoretically investigated. Then, using the Monte Carlo simulation, the rough surfaces with RD, RDSR, and RSOS models in [Formula: see text] dimensions are simulated in different growth times, and the Casimir force between each pair of rough surfaces in each time step is calculated. The results show that the force between the surfaces increases as the roughness increases.

CRYSTALLINE SPINON BASIS FOR RSOS MODELS

The crystalline spinon basis for the RSOS models associated with [Formula: see text] is studied. This basis gives fermionic type character formulas for the branching coefficients of the coset [Formula: see text]. In addition the path description of the parafermion characters is found as a limit of the spinon description of the string functions.