Boundary effect of a partition in a quantum well

We consider a system of identical particles, bosons or fermions, at finite temperatures confined in a one dimensional quantum well which has a partition in the center. Assuming nontrivial boundary conditions (Dirichlet on one side and Neumann on the other) for the partition, we study by numerical and analytic means the net pressure that emerges on the partition due to the difference in the energy levels between the two half wells separated by the partition. The quantum pressure has a single minimum in the medium temperature regime and exhibits a number of intriguing features, such as the scaling (square root) law for the diverging high temperature asymptotics and the distinctive dependences on the particle numbers characterizing the statistics of the particles. Our analytical approximations yield results which can account for these features and fit the numerical curves of the pressure reasonably well.