← Mathematical compendium
Published equation contexts
10−3
Why this formula appears here
Between those extremes sit two families with a gap between them. Engineered quantum simulators — cold-atom lattices, trapped-ion chains, Rydberg-atom arrays — cluster between 10^{-3} and 3×10^{-2} metres per second, because their dynamics run on tunnelling and spin-exchange rates measured in kilohertz, multiplied by lattice spacings measured in hundreds of nanometres. Natural crystals run several orders faster: longitudinal sound in ordinary crystalline silicon travels at 8.433 kilometres per second [ 12 ] ; the spin excitations of the near-ideal one-dimensional antiferromagnet potassium copper fluoride, with a measured exchange energy of 33.5 millielectronvolts, propagate at roughly…
Read the full article-specific guide →
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (3)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 21 · Crossed Fields
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Between those extremes sit two families with a gap between them. Engineered quantum simulators — cold-atom lattices, trapped-ion chains, Rydberg-atom arrays — cluster between 10^{-3} and 3×10^{-2} metres per second, because their dynamics run on tunnelling and spin-exchange rates measured in kilohertz, multiplied by lattice spacings measured in hundreds of nanometres. Natural crystals run several orders faster: longitudinal sound in ordinary crystalline silicon travels at 8.433 kilometres per second [ 12 ] ; the spin excitations of the near-ideal one-dimensional antiferromagnet potassium copper fluoride, with a measured exchange energy of 33.5 millielectronvolts, propagate at roughly…
Equation guide → ·
Article →Equation 7 · Evolutionary Physics
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Here Λ is what Joos and Zeh call the localization rate: a single number, with units of inverse length squared per unit time, built from the scattering cross-section of the object, the flux and momentum of whatever is doing the scattering, and nothing else [ 7 ] . Everything about how fast a given superposition dies is contained in Λ , and Λ is a number you can actually compute for a real object in a real environment — which is exactly what Joos and Zeh went on to do, in the paper’s Table 2, for three sizes of hypothetical “dust particle”: a large grain of radius 10^{-3} centimetres, a small grain of 10^{-5} centimetres, and a body of 10^{-6} centimetres that the paper…
Equation guide → ·
Article →Equation 35 · Quantum Information
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Gidney and Ekerå’s resource estimate makes the timing assumptions explicit rather than burying them: a planar grid with nearest-neighbour connectivity, a characteristic physical gate error rate of 10^{-3} , a surface code cycle time of 1 microsecond, and a reaction time of 10 microseconds [ 14 ] . That reaction time is the round trip from measurement to decoded decision to conditioned next gate. In their construction it is a first-class quantity in the runtime, not an implementation footnote.
Equation guide → ·
Article →