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Equation 6 · Part 4 · Every Crystal Has Its Own Speed of Light

Symbol C

∥[Ax(t),By]∥≤C e−(d(x,y)−cLR t)/ξ\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}
CC

What this part means

constants fixed by the microscopic couplings.

Its job in the formula

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

Where the article explains it

where C and ξ\xi are constants fixed by the microscopic couplings and d(x,y) is the distance between the two sites on the lattice [ 1 ] .

The passage around this formula

…lattice sites x and y , the size of their commutator after evolving one of them forward in time t is capped by an exponential in the distance between the sites minus the cone’s own reach: ∥[Ax(t),By]∥≤C e−(d(x,y)−cLR t)/ξ\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}. where C and ξ\xi are constants fixed by the microscopic couplings and d(x,y) is the distance between the two sites on the lattice [ 1 ] . Outside the cone, where d(x,y) exceeds cLRc_{\mathrm{LR}} t , the right-hand side collapses toward zero; inside it, the inequality simply has nothing to say. The velocity…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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