I Quantized Energy in micro scales

[3dot]

Say you had a crystal lattice box on a micro scale. You can push it with a bigger piston to accelerate it. Say it's lying on a friction-less surface (or this happens in minimal gravity and vacuum).

My question is, would the possible kinetic energy that you can impart on this cube be quantized? Or is this a large scale free particle question? I.e. are there are kinetic energies as a whole that this box literally cannot assume?

 

[muscaria]

I'm guessing by "bigger" piston you mean classical, right? Given that your box state will acquire momentum from a classical field, the centre of mass degree of freedom becomes delocalised without any further/external quantising boundary, by which I mean an external confining boundary which would discretise the allowable centre of mass momentum states. The centre of mass would then have a continuous range of accessible momentum states from $-\infty$ to $+\infty$. This was for the case where the spring could move also. If the spring is fixed on one side, then the amplitude for momentum states become damped for higher ranges but they will still form a continuum given that the spring piston itself does not "jump" between states. All this is assuming you are talking about a classical spring/piston though. That would be my take on your thought experiment anyway.

 

[muscaria]

Hmm.. came across something interesting after searching for related stuff. A paper came out a couple years ago relating to the system I think you had in mind: http://arxiv.org/pdf/1309.6354v2.pdf (Emergent Newtonian dynamics and the geometric origin of mass)
If you scroll down to around pg.20 you'll see the kind of systems you're talking about where they apparently find that the mass of the classical degree of freedom gets renormalised as it drags the quantum oscillators with it. Seems like an interesting paper which relates the emergence of mass at the classical limit to some distortion process of Hilbert space.

 

[3dot]

Yeah, the title and abstract seem to be what I am looking for, thanks. Now to actually study enough to understand it :D.