Adiabram: Adiabatic Theorem
Quantum Foundations arc, page 20 of 193. Back to The Pixelated Physics Universe
Who they are
Adiabram has one line, and says it often: “Change the scope slowly.”
Adiabram is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Adiabatic theorem: a system with a non-degenerate, gapped spectrum, changed slowly compared with ħ/ΔE, stays in its instantaneous eigenstate; sudden changes cause transitions.
$$ \begin{gathered} T_{\text{change}} \gg \frac{\hbar}{\Delta E} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $T_{\text{change}}$ | time scale of the change | s |
| $\hbar$ | reduced Planck constant | J·s |
| $\Delta E$ | energy gap to other states | J |
Sources
Crossovers
Adiabram meets Nutariel (Rabi Oscillation). Adiabram changes his system slowly compared with ħ/ΔE, and it stays in its eigenstate. Nutariel is driven on resonance, so her state does flop between levels. Whether a system changes state depends on how fast and at what frequency the push comes.
Adiabram meets Decouplarch (Born Oppenheimer Approximation). Decouplarch splits fast electrons from slow nuclei. That split rests on Adiabram's theorem: the nuclei move so slowly that the electrons follow, staying in their instantaneous state.
Wear the lore
Concept keywords: Adiabatic Theorem, Adiabram, Quantum Foundations, physics lore, Pixelated Physics