← Mathematical compendium

Published equation contexts

H(τ)H(\tau)

Why this formula appears here

The dossier for this paper flags something the two equations above do not, by themselves, settle: the periodic-evolution bound above was derived for a Hamiltonian with a genuinely time-independent spectrum. A real computation drives H(τ\tau) through a sequence of different instantaneous Hamiltonians, one per gate, and nothing guarantees in advance that a chain of instantaneously applied bounds sums to a valid bound on the whole chain. The condition that licenses treating N⊥N_\perp[Γ\Gamma] as a legitimate partition into instantaneously static Levitin-Toffoli steps is a quasi-static one: over one local orthogonalization time τML(τ)\tau_{\rm ML}(\tau) = π\piℏ\hbar/[2(⟨\langle H(τ\tau)⟩\rangle-E0(τ)E_0(\tau))] ,…

Read the full article-specific guide →

Read the representative guide

HH

Symbol H

H is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

H(τ)H(\tau)

Equation 34 · 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.

The dossier for this paper flags something the two equations above do not, by themselves, settle: the periodic-evolution bound above was derived for a Hamiltonian with a genuinely time-independent spectrum. A real computation drives H(τ\tau) through a sequence of different instantaneous Hamiltonians, one per gate, and nothing guarantees in advance that a chain of instantaneously applied bounds sums to a valid bound on the whole chain. The condition that licenses treating N⊥N_\perp[Γ\Gamma] as a legitimate partition into instantaneously static Levitin-Toffoli steps is a quasi-static one: over one local orthogonalization time τML(τ)\tau_{\rm ML}(\tau) = π\piℏ\hbar/[2(⟨\langle H(τ\tau)⟩\rangle-E0(τ)E_0(\tau))] ,…

Meanings in this article

  • τ\tau: a time, the integral has action units.
Equation guide → · Article →