1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
|
<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="groundstate.xsil" expected="groundstate_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5" />
<xsil_file name="groundstate_break.xsil" expected="groundstate_expected_break.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5" />
</testing>
<name>groundstate</name>
<author>Graham Dennis</author>
<description>
Calculate the ground state of a negative gaussian potential.
</description>
<features>
<auto_vectorise />
<benchmark />
<bing />
<fftw plan="patient" />
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="y" lattice="1024" domain="(-12.0, 12.0)" />
</transverse_dimensions>
</geometry>
<vector name="potential" initial_basis="y" type="complex">
<components>
V1
</components>
<initialisation>
<![CDATA[
real Vtrap = -exp(-y*y);
V1 = -i*Vtrap;
]]>
</initialisation>
</vector>
<vector name="wavefunction" initial_basis="y" type="complex">
<components>
phi
</components>
<initialisation>
<![CDATA[
// This will be automatically normalised later
phi = exp(-y*y);
]]>
</initialisation>
</vector>
<computed_vector name="normalisation" dimensions="" type="real">
<components> Ncalc </components>
<evaluation>
<dependencies basis="y">wavefunction</dependencies>
<![CDATA[
// Calculate the current normalisation of the wave function.
Ncalc = norm(phi);
]]>
</evaluation>
</computed_vector>
<sequence>
<integrate algorithm="RK4" interval="1.0" steps="1000">
<samples>50 50 50</samples>
<filters>
<filter>
<dependencies>wavefunction normalisation</dependencies>
<![CDATA[
// Correct normalisation of the wavefunction
phi *= sqrt(1.0/Ncalc);
]]>
</filter>
</filters>
<operators>
<operator kind="ip" constant="yes">
<operator_names>T</operator_names>
<![CDATA[
T = -0.5*ky*ky;
]]>
</operator>
<integration_vectors>wavefunction</integration_vectors>
<dependencies>potential</dependencies>
<![CDATA[
dphi_dt = T[phi] - (i*V1)*phi;
]]>
</operators>
</integrate>
<breakpoint filename="groundstate_break.xsil">
<dependencies>wavefunction potential</dependencies>
</breakpoint>
</sequence>
<output format="binary">
<group>
<sampling basis="y" initial_sample="no">
<moments>dens</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
dens = norm(phi);
]]>
</sampling>
</group>
<group>
<sampling initial_sample="no">
<moments>N</moments>
<dependencies>normalisation</dependencies>
<![CDATA[
N = Ncalc;
]]>
</sampling>
</group>
<group>
<sampling basis="y(0)" initial_sample="no">
<moments>N</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
N = norm(phi);
]]>
</sampling>
</group>
</output>
</simulation>
|
