<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>bessel_cosine_groundstate</name>
  <author>Graham Dennis</author>
  <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 />
    <benchmark />
    <bing />
    <chunked_output size="10KB" />
    <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>
      <!-- Volume prefactor = 2\pi is to cover the integration over \theta -->
      <dimension name="r" lattice="32"  domain="(0.0, 1.0e-5)" transform="bessel" volume_prefactor="2.0 * M_PI" />

      <!-- Volume prefactor = 2 is so that integration effectively runs from -1.0e-4 to +1.0e-4 -->
      <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>
  
  <vector name="wavefunction" type="complex">
    <components>
      phi
    </components>
    <initialisation>
      <![CDATA[
      
        if ((abs(r) < 0.9e-5) && abs(z) < 0.9e-4) {
          phi = 1.0; //sqrt(Nparticles/2.0e-5);
          // 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">
          <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 filename="bc_groundstate.xsil">
    <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>