  We calculate the quantum statistical force acting on a partition wall that
divides a one dimensional box into two halves. The two half boxes contain the
same (fixed) number of noninteracting bosons, are kept at the same temperature,
and admit the same boundary conditions at the outer walls; the only difference
is the distinct boundary conditions imposed at the two sides of the partition
wall. The net force acting on the partition wall is nonzero at zero temperature
and remains almost constant for low temperatures. As the temperature increases,
the force starts to decrease considerably, but after reaching a minimum it
starts to increase, and tends to infinity with a square-root-of-temperature
asympotics. This example demonstrates clearly that distinct boundary conditions
cause remarkable physical effects for quantum systems.

Quantum Physics