GenGellMann: Difference between revisions
Jump to navigation
Jump to search
Created page with "{{Function |name=GenGellMann |desc=Produces a generalized Gell-Mann operator |req=opt_args |rel=GellMann<br />GenPauli<br />Pauli |upd=December 18, 2013 |v=1.0..." |
No edit summary |
||
| Line 2: | Line 2: | ||
|name=GenGellMann | |name=GenGellMann | ||
|desc=Produces a generalized Gell-Mann operator | |desc=Produces a generalized Gell-Mann operator | ||
|rel=[[GellMann]]<br />[[GenPauli]]<br />[[Pauli]] | |rel=[[GellMann]]<br />[[GenPauli]]<br />[[Pauli]] | ||
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]] | |||
|upd=December 18, 2013 | |upd=December 18, 2013 | ||
|v= | |v=0.50}} | ||
<tt>'''GenGellMann'''</tt> is a [[List of functions|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices. | <tt>'''GenGellMann'''</tt> is a [[List of functions|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices. | ||
| Line 19: | Line 19: | ||
==Examples== | ==Examples== | ||
===Gives the Pauli operators when <tt>DIM = 2</tt>=== | ===Gives the Pauli operators when <tt>DIM = 2</tt>=== | ||
< | <syntaxhighlight> | ||
>> GenGellMann(0,0,2) % identity | >> GenGellMann(0,0,2) % identity | ||
| Line 47: | Line 47: | ||
1 0 | 1 0 | ||
0 -1 | 0 -1 | ||
</ | </syntaxhighlight> | ||
===Gives the Gell-Mann operators when <tt>DIM = 3</tt>=== | ===Gives the Gell-Mann operators when <tt>DIM = 3</tt>=== | ||
< | <syntaxhighlight> | ||
>> GenGellMann(0,1,3) | >> GenGellMann(0,1,3) | ||
| Line 74: | Line 74: | ||
0 0.5774 0 | 0 0.5774 0 | ||
0 0 -1.1547 | 0 0 -1.1547 | ||
</ | </syntaxhighlight> | ||
===In Higher Dimensions=== | ===In Higher Dimensions=== | ||
Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set <tt>SP = 1</tt> if <tt>DIM</tt> is large in order to save memory. | Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set <tt>SP = 1</tt> if <tt>DIM</tt> is large in order to save memory. | ||
< | <syntaxhighlight> | ||
>> GenGellMann(2,3,4) | >> GenGellMann(2,3,4) | ||
| Line 94: | Line 94: | ||
(206,35) 0.0000 + 1.0000i | (206,35) 0.0000 + 1.0000i | ||
(35,206) 0.0000 - 1.0000i | (35,206) 0.0000 - 1.0000i | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=GenGellMann}} | |||
==External links== | ==External links== | ||
* [http://en.wikipedia.org/wiki/Generalizations_of_the_Pauli_matrices Generalizations of the Pauli matrices] at Wikipedia | * [http://en.wikipedia.org/wiki/Generalizations_of_the_Pauli_matrices Generalizations of the Pauli matrices] at Wikipedia | ||
Revision as of 15:15, 29 September 2014
| GenGellMann | |
| Produces a generalized Gell-Mann operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | GellMann GenPauli Pauli |
| Function category | Special states, vectors, and operators |
GenGellMann is a function that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices.
Syntax
- G = GenGellMann(IND1,IND2,DIM)
- G = GenGellMann(IND1,IND2,DIM,SP)
Argument descriptions
- IND1 and IND2: Integers between 0 and DIM-1, inclusive. If IND1 == IND2 then G will be diagonal. If IND1 < IND2 then G will be real and have exactly 2 nonzero entries. If IND1 > IND2 then G will be imaginary and have exactly 2 nonzero entries.
- DIM: The size of the output matrix.
- SP (optional, default 0): A flag (either 1 or 0) indicating that the generalized Gell-Mann matrix produced should or should not be sparse.
Examples
Gives the Pauli operators when DIM = 2
>> GenGellMann(0,0,2) % identity
ans =
1 0
0 1
>> GenGellMann(0,1,2) % Pauli X
ans =
0 1
1 0
>> GenGellMann(1,0,2) % Pauli Y
ans =
0.0000 + 0.0000i 0.0000 - 1.0000i
0.0000 + 1.0000i 0.0000 + 0.0000i
>> GenGellMann(1,1,2) % Pauli Z
ans =
1 0
0 -1Gives the Gell-Mann operators when DIM = 3
>> GenGellMann(0,1,3)
ans =
0 1 0
1 0 0
0 0 0
>> GenGellMann(0,2,3)
ans =
0 0 1
0 0 0
1 0 0
>> GenGellMann(2,2,3)
ans =
0.5774 0 0
0 0.5774 0
0 0 -1.1547In Higher Dimensions
Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set SP = 1 if DIM is large in order to save memory.
>> GenGellMann(2,3,4)
ans =
0 0 0 0
0 0 0 0
0 0 0 1
0 0 1 0
>> GenGellMann(205,34,500,1) % a 500-by-500 sparse generalized Gell-Mann matrix
ans =
(206,35) 0.0000 + 1.0000i
(35,206) 0.0000 - 1.0000iSource code
Click here to view this function's source code on github.
External links
- Generalizations of the Pauli matrices at Wikipedia