The Influence of Surface Roughness on Equilibrium States of Superfluid $\text{}^{3}$He in Confined Geometry

The superfluid $\text{}^{3}$He is considered in confined geometry for arbitrary thickness when surface roughness is taken into account. The equilibrium states, the critical size when the two-dimensional state is realized exclusively, and the critical thickness below which superfluidity is destroyed are defined, found and discussed with reference to the essential parameters of a system. Some particular cases are examined analytically. The examples of exact numerical solutions are presented.