Quantized Energy in micro scales

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Discussion Overview

The discussion revolves around the concept of quantized energy in a micro-scale system, specifically focusing on a crystal lattice box subjected to external forces, such as a piston. Participants explore whether the kinetic energy imparted to this system is quantized or if it behaves like a classical free particle, questioning the nature of kinetic energy states available to the box.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether the kinetic energy of a micro-scale crystal lattice box can be quantized or if it behaves as a classical free particle, suggesting there may be kinetic energies that the box cannot assume.
  • Another participant interprets the question as involving a classical piston and argues that without an external confining boundary, the center of mass of the box would have a continuous range of accessible momentum states, implying no quantization in that scenario.
  • A different participant references a related paper that discusses the emergence of mass and its relation to quantum oscillators, suggesting that the classical limit may involve renormalization processes that could be relevant to the original question.
  • One participant expresses interest in the referenced paper, indicating a desire to understand its implications for the discussion.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the nature of kinetic energy in the proposed system, with no consensus reached on whether the energy states are quantized or continuous.

Contextual Notes

The discussion is limited by assumptions about the nature of the piston and the system's boundaries, as well as the dependence on classical versus quantum mechanical interpretations.

3dot
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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?
 
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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.
 
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.
 
Yeah, the title and abstract seem to be what I am looking for, thanks. Now to actually study enough to understand it :D.
 

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