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⟨H⟩−E0\langle H\rangle-E_0

Why this formula appears here

where ⟨\langle H⟩\rangle is the mean energy in the evolving state and E0E_0 is the ground-state energy of H [ 2 , 1 ] . Inverting this gives a maximum rate of orthogonal state changes per unit proper time, 2(⟨\langle H⟩\rangle-E0E_0)/π\piℏ\hbar , and Giovannetti, Lloyd, and Maccone showed that for a periodic evolution this rate integrates cleanly: a system with mean energy ⟨\langle H⟩\rangle-E0E_0 above its ground state can pass through at most

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HH

Symbol H

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⟨H⟩−E0\langle H\rangle-E_0

Equation 14 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where ⟨\langle H⟩\rangle is the mean energy in the evolving state and E0E_0 is the ground-state energy of H [ 2 , 1 ] . Inverting this gives a maximum rate of orthogonal state changes per unit proper time, 2(⟨\langle H⟩\rangle-E0E_0)/π\piℏ\hbar , and Giovannetti, Lloyd, and Maccone showed that for a periodic evolution this rate integrates cleanly: a system with mean energy ⟨\langle H⟩\rangle-E0E_0 above its ground state can pass through at most

Meanings in this article

  • E0E_0: the ground-state energy of H [ 2 , 1 ].
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