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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="bessel_cosine_stochastic_groundstate.xsil" expected="bessel_cosine_stochastic_groundstate_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
</testing>
<author>Graham Dennis</author>
<name>bessel_cosine_stochastic_groundstate</name>
<description>
Calculate the 3D ground state of a Rubidium BEC in a harmonic magnetic trap assuming
cylindrical symmetry about the z axis and reflection symmetry about z=0.
This permits us to use the cylindrical bessel functions to expand the solution transverse
to z and a cosine series to expand the solution along z.
</description>
<features>
<auto_vectorise />
<chunked_output size="100KB" />
<globals>
<![CDATA[
const real omegaz = 2*M_PI*20;
const real omegarho = 2*M_PI*200;
const real hbar = 1.05457148e-34;
const real M = 1.409539200000000e-25;
const real g = 9.8;
const real scatteringLength = 5.57e-9;
const real Uint = 4.0*M_PI*hbar*hbar*scatteringLength/M;
const real Nparticles = 5.0e5;
/* offset constants */
const real EnergyOffset = pow(15.0*Nparticles*Uint*omegaz*omegarho*omegarho/(8*M_PI), 2.0/5.0)
* pow(M/2.0, 3.0/5.0);
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="r" lattice="32" domain="(0.0, 1.0e-5)" transform="bessel" volume_prefactor="2.0*M_PI" />
<dimension name="z" lattice="32" domain="(0.0, 1.0e-4)" transform="dct" volume_prefactor="2.0" />
</transverse_dimensions>
</geometry>
<vector name="potential" type="complex">
<components>
V1
</components>
<initialisation>
<![CDATA[
real Vtrap = 0.5*M*(omegarho*omegarho*r*r + omegaz*omegaz*z*z);
V1 = -i/hbar*(Vtrap - EnergyOffset);
]]>
</initialisation>
</vector>
<noise_vector name="noise" kind="gaussian" method="solirte" type="complex" seed="15687 65687 684320 4057 354">
<components>eta</components>
</noise_vector>
<vector name="wavefunction" type="complex">
<components>
phi
</components>
<initialisation>
<dependencies>noise</dependencies>
<![CDATA[
if ((abs(r) < 0.9e-5) && abs(z) < 0.9e-4) {
phi = eta;
// This will be automatically normalised later
} else {
phi = 0.0;
}
]]>
</initialisation>
</vector>
<computed_vector name="normalisation" dimensions="" type="real">
<components>
Ncalc
</components>
<evaluation>
<dependencies>wavefunction</dependencies>
<![CDATA[
// Calculate the current normalisation of the wave function.
Ncalc = mod2(phi);
]]>
</evaluation>
</computed_vector>
<sequence>
<integrate algorithm="RK4" interval="1e-4" steps="1000">
<samples>100</samples>
<filters>
<filter>
<dependencies>wavefunction normalisation</dependencies>
<![CDATA[
// Correct normalisation of the wavefunction
phi *= sqrt(Nparticles/Ncalc);
]]>
</filter>
</filters>
<operators>
<operator kind="ip" constant="yes">
<operator_names>T</operator_names>
<![CDATA[
T = -0.5*hbar/M*(kr*kr + kz*kz);
]]>
</operator>
<integration_vectors>wavefunction</integration_vectors>
<dependencies>potential</dependencies>
<![CDATA[
dphi_dt = T[phi] - (i*V1 + Uint/hbar*mod2(phi))*phi;
]]>
</operators>
</integrate>
</sequence>
<output format="hdf5">
<sampling_group basis="r z" initial_sample="no">
<moments>norm_dens</moments>
<dependencies>wavefunction normalisation</dependencies>
<![CDATA[
norm_dens = mod2(phi)/Ncalc;
]]>
</sampling_group>
</output>
</simulation>
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