We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.

In the spirit of the thin-layer quantization scheme, we give the effective Shrödinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells reconstructed by the corrugation not being at identical depths, which is strikingly different from that of a corrugated nanotube, especially in the inner side of the torus. By numerically calculating the transmission probability, we find that the resonant tunneling peaks and the transmission gaps are merged and broadened by the corrugation of the inner side of torus. These results show that the quarter corrugated torus can be used not only to connect two tubes with different radiuses in different directions, but also to filter the particles with particular incident energies.