The word quasiparticle is a term of art that condensed matter physics types throw around quite a bit. What does is it really mean? I'll describe one analogy that may be useful, and then give a more rigorous definition. Suppose you had a bin filled up to some height with rubber balls of uniform size. The lowest energy ("ground") state of this would be the one with the balls pretty much forming a close-packed structure, all stacked up. If you took one ball from somewhere and set it on top of the others, that would cost a little bit of energy, because the ball has some mass acted on by gravity and it takes work to lift it up. This one ball popped up above the rest is not exactly a quasiparticle. Notice that it's not really the same as an isolated ball. It's a bit deformed from interactions with the balls underneath it, since it has weight and the balls are all a little squishy. Similarly, if you took a step back and looked really carefully, you'd see that the balls right under that one have all had to rearrange themselves a little. The whole package (popped-up ball + deformations + rearrangement of the positions of the neighboring balls) is analogous to a quasiparticle, since you can't really have some parts without the others. In condensed matter physics, a fancier scientific definition would be: "a low energy excitation of a system, possessing a set of quantum numbers and/or well-defined expectation values of certain operators (position, charge, momentum, angular momentum, energy) often associated with isolated particles."
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