Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
NambuUnitary  |  |
|
| | ||||
Details and Options
Examples
(6)
Basic Examples
(5)
Consider some fermion modes.
In[1]:=
$n=4;
Construct an initial state.
In[2]:=
in=WickState[{1,0},$n]
Out[2]=
WickState
 |
|
In[3]:=
SeedRandom[354];
In[4]:=
wu=RandomNambuUnitary[$n]
Out[4]=
NambuUnitary
|
|
In[5]:=
barU=Normal[wu];barU//ArrayShortbarU.Topple[barU]//Chop//ArrayShort
Out[5]//MatrixForm=
-0.29782+0.0701004 | 0.368911+0.21472 | -0.306222-0.0531149 | 0.415105-0.0586185 | … |
-0.214518-0.194513 | -0.0545964-0.358606 | -0.470166-0.25852 | -0.257193-0.242454 | … |
-0.276196+0.0100007 | -0.100239+0.478109 | -0.241555+0.208507 | -0.201799-0.326542 | … |
0.062476+0.341379 | -0.421002+0.11886 | 0.0330062-0.338269 | -0.106553+0.1523 | … |
… | … | … | … | … |
Out[5]//MatrixForm=
1 | 0 | 0 | 0 | … |
0 | 1 | 0 | 0 | … |
0 | 0 | 1 | 0 | … |
0 | 0 | 0 | 1 | … |
… | … | … | … | … |
In[6]:=
out=wu**in
Out[6]=
WickState
|
|
In[7]:=
Norm[out]//Chop
Out[7]=
1
In[1]:=
$n=4;
In[2]:=
SeedRandom[354];
Recall that in order to avoid redundancy, only keeps the independent blocks U and V of the full unitary matrix, :=
.
U
U | V |
* V | * U |
In[3]:=
wu=RandomNambuUnitary[$n]wu//ArrayShort
Out[3]=
NambuUnitary
|
|
Out[3]=
,
-0.29782+0.0701004 | 0.368911+0.21472 | -0.306222-0.0531149 | 0.415105-0.0586185 |
-0.214518-0.194513 | -0.0545964-0.358606 | -0.470166-0.25852 | -0.257193-0.242454 |
-0.276196+0.0100007 | -0.100239+0.478109 | -0.241555+0.208507 | -0.201799-0.326542 |
0.062476+0.341379 | -0.421002+0.11886 | 0.0330062-0.338269 | -0.106553+0.1523 |
0.176701-0.0352446 | 0.188394+0.20583 | -0.356562+0.376824 | -0.232192-0.135932 |
0.338876+0.305656 | -0.0361622+0.173385 | 0.118451-0.257026 | -0.219913+0.0604959 |
-0.543984+0.225341 | 0.139794+0.16616 | 0.155693-0.0674951 | 0.111754-0.0258787 |
-0.147337+0.128743 | 0.217871-0.228839 | -0.0166458+0.140999 | -0.615459-0.0325303 |
converts it to the full matrix.
In[4]:=
barU=Normal[wu];barU//ArrayShort
Out[4]//MatrixForm=
-0.29782+0.0701004 | 0.368911+0.21472 | -0.306222-0.0531149 | 0.415105-0.0586185 | … |
-0.214518-0.194513 | -0.0545964-0.358606 | -0.470166-0.25852 | -0.257193-0.242454 | … |
-0.276196+0.0100007 | -0.100239+0.478109 | -0.241555+0.208507 | -0.201799-0.326542 | … |
0.062476+0.341379 | -0.421002+0.11886 | 0.0330062-0.338269 | -0.106553+0.1523 | … |
… | … | … | … | … |
In[5]:=
new=NambuUnitary[barU]
Out[5]=
NambuUnitary
|
|
In[6]:=
new-wu//Chop//MatrixForm
Out[6]=
,
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
In[1]:=
$n=4;
In[2]:=
SeedRandom[354];
If you can working in the normal space (not the Nambu space), then give to set the upper-right block to the zero matrix.
{u,0}
In[3]:=
u=RandomUnitary[$n];u//MatrixForm
Out[3]//MatrixForm=
0.248696-0.151076 | 0.222527+0.283521 | 0.462696-0.281419 | 0.369733+0.596186 |
-0.153909-0.13342 | -0.279898+0.502144 | 0.320992+0.402601 | 0.425217-0.426717 |
0.504483-0.746275 | 0.157214+0.13215 | -0.168049+0.146213 | -0.270274-0.154023 |
0.0688615-0.240137 | -0.633685-0.309629 | 0.426546-0.458293 | -0.150427-0.159885 |
In[4]:=
wu=NambuUnitary[{u,0}];wu//ArrayShort
Out[4]=
,
0.248696-0.151076 | 0.222527+0.283521 | 0.462696-0.281419 | 0.369733+0.596186 |
-0.153909-0.13342 | -0.279898+0.502144 | 0.320992+0.402601 | 0.425217-0.426717 |
0.504483-0.746275 | 0.157214+0.13215 | -0.168049+0.146213 | -0.270274-0.154023 |
0.0688615-0.240137 | -0.633685-0.309629 | 0.426546-0.458293 | -0.150427-0.159885 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
In[5]:=
new=NambuUnitary[{u,Zero[{$n,$n}]}]
Out[5]=
NambuUnitary
|
|
In[6]:=
wu-new//Chop//MatrixForm
Out[6]=
,
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
In[1]:=
$n=4;
In[2]:=
SeedRandom[354];
In[3]:=
foo=RandomNambuUnitary[$n]bar=RandomNambuUnitary[$n]
Out[3]=
NambuUnitary
|
|
Out[3]=
NambuUnitary
|
|
In[4]:=
new=3*foo-2*bar
Out[4]=
NambuUnitary
|
|
In[5]:=
3*First[foo]-2*First[bar]-First[new]//Chop//Map[MatrixForm]
Out[5]=
,
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 |
In[6]:=
new=Dagger[foo]
Out[6]=
NambuUnitary
|
|