Difference between revisions of "Weyl.m"
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{{DISPLAYTITLE:weyl.m}} __NOTOC__ | {{DISPLAYTITLE:weyl.m}} __NOTOC__ | ||
| − | Weyl boson operators (sparse, see below for normalisa- tion convention) for a bosonic mode with a user- | + | Weyl boson operators (sparse, see below for normalisa- tion convention) for a bosonic mode with a user-speci- |
==Syntax== | ==Syntax== | ||
| Line 17: | Line 17: | ||
A.a - annihilation operator | A.a - annihilation operator | ||
A.n - population number operator | A.n - population number operator | ||
| + | Note: the matrices are normalised to obey the following | ||
| + | relations for all energy level counts | ||
| + | A.c*A.a=A.n, [A.n,A.c]=A.c | ||
| + | [A.n,A.a]=-A.a, [A.a,A.c]=A.u | ||
| + | except for the edge state at which [A.a,A.c] ele- | ||
| + | ment is (1-nlevels), this is unavoidable. | ||
| + | Note: arrays are declared complex at build time to avoid | ||
| + | expensive reallocation operations later on. | ||
==Examples== | ==Examples== | ||
| Line 25: | Line 33: | ||
==See also== | ==See also== | ||
| − | [[ | + | * [[boson_mono.m]] |
| + | * [[boson_ortho.m]] | ||
| + | * [[bos_product_table.m]] | ||
| + | * [[enlev2bm.m]] | ||
| + | * [[oper2bm.m]] | ||
| + | * [[kq2lin.m]] | ||
| + | |||
| + | |||
''Version 2.11, authors: [[Ilya Kuprov]]'' | ''Version 2.11, authors: [[Ilya Kuprov]]'' | ||
Revision as of 21:37, 22 February 2026
Weyl boson operators (sparse, see below for normalisa- tion convention) for a bosonic mode with a user-speci-
Syntax
A=weyl(nlevels)
Arguments
nlevels - an integer specifying the
number of population levels
Outputs
A.u - unit operator
A.c - creation operator
A.a - annihilation operator
A.n - population number operator
Note: the matrices are normalised to obey the following
relations for all energy level counts
A.c*A.a=A.n, [A.n,A.c]=A.c
[A.n,A.a]=-A.a, [A.a,A.c]=A.u
except for the edge state at which [A.a,A.c] ele-
ment is (1-nlevels), this is unavoidable.
Note: arrays are declared complex at build time to avoid
expensive reallocation operations later on.
Examples
See examples in the Spinach distribution relevant to this function.
Notes
This page was generated from the function header in the Spinach repository.
See also
Version 2.11, authors: Ilya Kuprov
