weyl sequence

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The constellation of the spreading sequence based on Weyl sequence

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Splitting of a doubleWeyl point in two singleWeyl points in presence

Splitting of a doubleWeyl point in two singleWeyl points in presence

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Hermann Weyl Stanford Encyclopedia of Philosophy

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FIG S3 Weyl points and regions with the nonzero winding number Wik

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The minimal Weyl semimetal model a Spectral function at y Ly 1

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The topological phase diagram of the Weyl semimetal at large tilt

Figure 1 from Pressure driven Weyltopological insulator phase

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In mathematics, a Weyl sequence is a sequence from the equidistribution theorem proven by Hermann Weyl:
The sequence of all multiples of an irrational α,

0, α, 2α, 3α, 4α, ...
is equidistributed modulo 1.
In other words, the sequence of the fractional parts of each term will be uniformly distributed in the interval [0, 1).




In computing


In computing, an integer version of this sequence is often used to generate a discrete uniform distribution rather than a continuous one. Instead of using an irrational number, which cannot be calculated on a digital computer, the ratio of two integers is used in its place. An integer k is chosen, relatively prime to an integer modulus m. In the common case that m is a power of 2, this amounts to requiring that k is odd.
The sequence of all multiples of such an integer k,

0, k, 2k, 3k, 4k, …
is equidistributed modulo m.
That is, the sequence of the remainders of each term when divided by m will be uniformly distributed in the interval [0, m).
The term appears to originate with George Marsaglia’s paper "Xorshift RNGs".
The following C code generates what Marsaglia calls a "Weyl sequence":

d += 362437;
In this case, the odd integer is 362437, and the results are computed modulo m = 232 because d is a 32-bit quantity. The results are equidistributed modulo 232.




See also


List of things named after Hermann Weyl




References

Kata Kunci Pencarian: weyl sequence

• Ledakan Dahsyat
• Vladimir Arnold
• Weyl sequence
• Equidistributed sequence
• List of random number generators
• Pseudorandom number generator
• Spinor
• Random number generation
• Middle-square method
• List of things named after Hermann Weyl
• Linear congruential generator
• Xorshift