I Localization of particles and disorder at the quantum level?

[asimov42]

Hi all,

Based on a previous post on Anderson Localization, I'm posting a more general question here: given that there is substantial disorder in many systems in general (e.g., the body, or the Earth), why do we not see effects like Anderson Localization more frequently - that is, why aren't particle wave functions often confined to specific, limited regions of spacetime? I would think that, given that there are potential barriers in essentially random locations everywhere (not quite 'particle in a box', but similar), why does this not force the localization of particles (which I realize are field excitations) to small regions (in a similar fashion to the Anderson model) all over the place?

The human body is, for example, conductive, so clearly electrons are not constrained to move and the wave functions can diffuse, although there are potential barriers that exist. If we were to consider, say, the path integral formulation, is it simply the case that the phases of the possible paths of an individual electron interfere in such a way that conduction is possible? Despite the disorder that should constrain the diffusion? (or perhaps does, but only to some extent?)

 

[mfb]

Most electrons in most systems are bound to atoms. Only a small number (typically 1-2 per atom in metals) has a wave function that is spread out. In bad conductors like human tissue, a very small fraction of electrons contributes to conductivity, and does that by "hopping" from molecule to molecule, staying quite localized all the time, just with a changing position. Some ions contribute as well.

 

[asimov42]

The mfb! That's helpful - I think my question is even more general however: why don't we see confinement of, e.g., an electron, due to large scale disorder (potential barriers and wells)? Is it simply that the wave functions of the particles involved interfere in such as way as to allow conduction of the electron (in a liquid / solid) or diffusion? The Anderson model would say that every potential barrier / well should contribute to localizing the electron.

Perhaps an easier question: since the wave function for e.g., the electron, is spread out from a 'peak', matter farther and farther away should have a lesser and lesser effect on the wave function (this a naive question that comes from a lack of understanding, so I apologize)? E.g., if we have electrons, at, say, opposite sides of the Earth, their influence on each other should be negligible.

Thanks!

 

[BvU]

E.g., if we have electrons, at, say, opposite sides of the Earth, their influence on each other should be negligible.

You're very right there! But it doesn't take that much distance at all: intracellular distances are already enough. Subcellular too. Intermolecular distances probably also, but I don't know all the details about the conditions for this Anderson effect.

 

[mfb]

Decoherence ruins every approach of getting macroscopic wavefunctions in materials like human tissue.

 

[asimov42]

Ok, so the Anderson Localization model would say that above a certain level of disorder, particle wave functions are confined to finite regions. I assume then, that there is insufficient disorder in many cases (like the human body) for this to occur (clearly there must be on nothing could conduct). Maybe DrDu can shed some light, from the original thread https://www.physicsforums.com/threads/anderson-localization-and-general-disorder-of-matter.888063/ ?