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Re: [Phys-l] distinguishability



On 07/15/2011 07:15 PM, Carl Mungan wrote:
1. Is there a difference between a "classical ideal gas" and an
"ideal gas of classical particles"?

My reasoning for thinking the answer might be yes is that it seems to
me there are 3 relevant length scales: the thermal de Broglie length
(L), the size of a gas particle (R), and the average distance between
gas particles (D).

I'm not 100% comfortable with that terminology, but (as always)
we don't need to fuss over the terminology, when there is real
physics to be had.

Here's where the rubber meets the road:

classical ideal gas: one for which D >> L [a]
ideal gas of classical particles: one for which R >> L [b]

Short answer: Yes. Those two cases are quite definitely different.

Slightly longer answer:

If requirement [b] is violated, the individual scattering events
are quantum mechanical. The particles are not hard little particles
that bounce off each other, but rather big fluffy clouds that pass
through each other and diffract off each other. The consequences
can be spectacular, even if [b] is only weakly violated.

Reference, with memorable spin-wave spectrum:
B.R. Johnson et al.
"Observation of Nuclear Spin Waves in Spin-Polarized Atomic Hydrogen Gas"
http://prl.aps.org/abstract/PRL/v52/i17/p1508_1


Suggestions on the terminology:
*) Requirement [a] says that the gas is _non-degenerate_.

*) It is generally best to avoid using the word "classical" without
qualification, because it can mean so many different things:
-- non-relativistic
-- non-degenerate
-- et cetera

*) I'm not entirely sure what is a good term for requirement [b].
Maybe the _classical scattering regime_ or some such.