For example, in a superfluid, both the " U ( 1 ) " particle number symmetry and Galilean symmetry are spontaneously broken.
32.
This explains why the " particle numbers ", which are defined in terms of the creation and annihilation operators, are different in both coordinates.
33.
The following table lists various thermodynamic quantities calculated in the limit of low temperature and high temperature, and in the limit of infinite particle number.
34.
As a result, the grand canonical ensemble can be highly inaccurate when applied to small systems of fixed particle number, such as atomic nuclei.
35.
For systems where the particle number is variable ( due to contact with a particle reservoir ), the correct description is the grand canonical ensemble.
36.
It turns out, however, that the above equation for particle number expresses the number of bosons in excited states rather well, and thus:
37.
The truth of this statement for volume is trivial, for particles one might say that the total particle number of each atomic element is conserved.
38.
What is the frequency of particle collisions in an ideal gas, given the standard parameters ( particle number, pressure, volume, temperature )?
39.
Since all levels of expectation values can be nonzero, up to the actual particle number, this equation cannot be directly truncated without further considerations.
40.
For example, for a thermodynamic system consisting of a piston containing water vapour, the particle number is the number of water molecules in the system.
