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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="hermitegauss_transform_2d.xsil" expected="hermitegauss_transform_2d_expected.xsil" absolute_tolerance="1e-8" relative_tolerance="1e-5" />
</testing>
<name>hermitegauss_transform_2d</name>
<author>Graham Dennis</author>
<description>
Solve the Schroedinger equation in 2D using the hermite-Gauss basis.
</description>
<features>
<benchmark />
<!-- <error_check /> -->
<bing />
<!-- <fftw plan="estimate" /> -->
<mmt />
<validation kind="run-time" />
<globals>
<![CDATA[
const double M = 9.1e-31; // Mass of an electron
const double hbar = 1.05e-34;
const double omega = 2*M_PI*1e3;
const double offset = 1.0 * sqrt(hbar/(M*omega));
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="20" length_scale="sqrt(hbar/(M*omega))" transform="hermite-gauss" />
<dimension name="y" lattice="20" length_scale="sqrt(hbar/(M*omega))" transform="hermite-gauss" />
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x y" type="complex">
<components>
psi
</components>
<initialisation>
<![CDATA[
// initial state is the groundstate in the x axis, but shifted by offset
psi = pow(M*omega/(hbar*M_PI), 0.25) * exp(-0.5*(M*omega/hbar)*(x - offset)*(x - offset));
// and an expanded gaussian in the y axis
psi *= pow(M*omega/(hbar*M_PI), 0.25) * exp(-0.25*(M*omega/hbar)*y*y);
]]>
</initialisation>
</vector>
<computed_vector name="normalisation" dimensions="" type="double">
<components>N integral_y2</components>
<evaluation>
<dependencies>main</dependencies>
<![CDATA[
N = mod2(psi);
integral_y2 = mod2(psi)*y*y;
]]>
</evaluation>
</computed_vector>
<sequence>
<integrate algorithm="ARK45" tolerance="1e-6" interval="1e-3" steps="400">
<samples>10 1 100</samples>
<operators>
<operator kind="ip" constant="yes" fourier_space="nx ny">
<operator_names>L</operator_names>
<![CDATA[
L = -i*(nx + ny + 1.0)*omega;
]]>
</operator>
<integration_vectors>main</integration_vectors>
<![CDATA[
dpsi_dt = L[psi];
]]>
</operators>
</integrate>
</sequence>
<output format="binary">
<sampling_group initial_sample="yes">
<dimension name="x" fourier_space="no" />
<dimension name="y" fourier_space="no" />
<moments>dens</moments>
<dependencies>main</dependencies>
<![CDATA[
dens = mod2(psi);
]]>
</sampling_group>
<sampling_group initial_sample="no">
<dimension name="x" fourier_space="yes" />
<dimension name="y" fourier_space="yes" />
<moments>dens</moments>
<dependencies>main</dependencies>
<![CDATA[
dens = mod2(psi);
]]>
</sampling_group>
<sampling_group initial_sample="yes">
<dimension name="x" lattice="0" />
<dimension name="y" lattice="0" />
<moments>mean_x mean_sigmay</moments>
<dependencies>main normalisation</dependencies>
<![CDATA[
mean_x = mod2(psi)*x/N;
mean_sigmay = sqrt(integral_y2/N);
]]>
</sampling_group>
</output>
<info>
Script compiled with xpdeint version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
See http://www.xmds.org for more information.
</info>
<XSIL Name="moment_group_1">
<Param Name="n_independent">3</Param>
<Array Name="variables" Type="Text">
<Dim>4</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t x y dens
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>11</Dim>
<Dim>20</Dim>
<Dim>20</Dim>
<Dim>4</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="BigEndian"/>
hermitegauss_transform_2d_expected_mg0.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_2">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
nx ny dens
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>20</Dim>
<Dim>20</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="BigEndian"/>
hermitegauss_transform_2d_expected_mg1.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_3">
<Param Name="n_independent">1</Param>
<Array Name="variables" Type="Text">
<Dim>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t mean_x mean_sigmay
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>101</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="BigEndian"/>
hermitegauss_transform_2d_expected_mg2.dat
</Stream>
</Array>
</XSIL>
</simulation>
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