Quantum Entanglement - Revision history

Jess at 22:49, 17 September 2022

2022-09-17T22:49:40Z

Jess at 22:39, 17 September 2022

2022-09-17T22:39:45Z

Jess: Created page with "Relaxonomy --> here ---- Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby pa..."

2022-09-17T22:35:00Z

Created page with "Relaxonomy --> here ---- Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby pa..."

New page

[[Relaxonomy]] --> here
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Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby particles, either nuclei or electrons. (I count atomic orbitals with nonzero angular momentum as "electrons".) But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin. In reality, all the coupled spins evolve together until interrupted by fluctuations or hopping. The result is most vividly obvious when the muon captures a single electron to form the [[Muonium]] atom, which see. But it is also clearly evident in cases where the muon couples to a small number of spin-1/2 nuclei, as in fluoride insulators, where the <math>\mu^+</math> takes up a position between two <SUP>19</SUP>F nuclei and the 3-spin system exhibits oscillations at three characteristic frequencies in ZF:

<center>
[[Image:FmuFx3.png|600px|inline image (click to see full size)]]
{| width="80%"
! align="center" |
Characteristic "FµF" signals in a variety of insulating fluorides.|}
</center>

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 Characteristic "F&micro;F" signals in a variety of insulating fluorides.|}
 </center>
+The role of <SUP>19</SUP>F in such coupled evolution can be played by any spin-1/2 nucleus, but few have a large enough magnetic moment or are sufficiently near the &micro;<SUP>+</SUP> to show themselves so vividly.
+However, even a system as complicated as the &micro;<SUP>+</SUP> surrounded by 8 copper nuclei in the octahedral site exhibits enhanced relaxation when the muon's Zeeman splitting matches the electric quadrupolar splitting of the Cu nuclei in the muon's electric field.  This phenomenon is known as [[Resonant Relaxation]], which see.

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-Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby particles, either nuclei or electrons.  (I count atomic orbitals with nonzero angular momentum as "electrons".)  But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin.  In reality, all the coupled spins evolve together until interrupted by fluctuations or hopping.  The result is most vividly obvious when the muon captures a single electron to form the [[Muonium]] atom, which see.  But it is also clearly evident in cases where the muon couples to a small number of spin-1/2 nuclei, as in fluoride insulators, where the <math>\mu^+</math> takes up a position between two <SUP>19</SUP>F nuclei and the 3-spin system exhibits oscillations at three characteristic frequencies in ZF:
+Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby particles, either nuclei or electrons.  (I count atomic orbitals with nonzero angular momentum as "electrons".)  But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin.  In reality, all the coupled spins evolve together until interrupted by fluctuations or muon hopping.
+The result is most vividly obvious when the muon captures a single electron to form the [[Muonium]] atom, which see.
+But it is also clearly evident in cases where the muon couples to a small number of spin-1/2 nuclei, as in fluoride insulators, where the <math>\mu^+</math> takes up a position between two <SUP>19</SUP>F nuclei and the 3-spin system exhibits oscillations at three characteristic frequencies in ZF:
 <center>