breathingMode.xmds

<?xml version="1.2"?>
<!--  Non-Linear (GPE like) S.E. for 1-D BEC at T=0, with a harm. osc. potential  -->

<simulation>

  <name>breathingMode</name>
  <author>Magnus Ogren</author>
  <description>
    Example of how XMDS can use consecutive integration sections and an
    external real-parameter (mygamma).
    This code has been used to calculate breathingmode ratios for 1D BEC at
    T=0 in the intermediate interaction regime.
  </description>

  <prop_dim>t</prop_dim>
  <error_check>yes</error_check>
  <stochastic>no</stochastic>

  <argv>
    <arg>
      <name>mygamma</name>
      <type>double</type>
      <default_value>0.01</default_value>
    </arg>
  </argv>

  <globals>
  <![CDATA[
    const double mu = 1000.0;
    const double w = 10.0;
    const double m = 1.0;
    const double hbar = 1.0;

    // Constants from the fitting to L & L:s equation of states 
    const double A = 1.886092;
    const double B = 0.1139075;
    const double C = 0.09556450;
    const double D = 39.5544355;
  ]]>
  </globals>

  <field>
    <name>main</name>
    <dimensions>  x   </dimensions>
    <lattice>   600  </lattice>
    <domains>  (-15,15) </domains>
    <samples>1</samples>
    <vector>
      <name>main</name>
      <type>complex</type>
      <components>phi</components>
      <fourier_space>no</fourier_space>
      <![CDATA[
        if (abs(x)<4.0)
          phi =sqrt( 1*(1-x*x*0.04) ) ;
        else 
          phi =0.0;
      ]]>
    </vector>
  </field>

  <sequence>
    <integrate>
      <algorithm>RK4IP</algorithm>
      <interval>0.5</interval>
      <lattice>5000</lattice>
      <samples>2500</samples>
      <k_operators>
        <constant>no</constant>
        <operator_names>L1</operator_names>
        <![CDATA[
          L1 = rcomplex(-kx*kx*0.5,0);
        ]]>
      </k_operators>
      <![CDATA[
        dphi_dt = L1[phi]*hbar*hbar/m   -0.5*m*w*w*x*x*phi +mu*phi
                  - hbar*hbar*0.5/m*2/mygamma*( 2*mod2(phi) 
                  - 2/mygamma*( A*C*log( 1/C*mygamma/2*mod2(phi) +1 ) 
                  +  B*D*log( 1/D*mygamma/2*mod2(phi) + 1 ) ) )*phi  ; 
      ]]>
    </integrate>

    <integrate>
      <algorithm>RK4IP</algorithm>
      <interval>2.5</interval>
      <lattice>25000</lattice>
      <samples>12500</samples>
      <k_operators>
        <constant>yes</constant>
        <operator_names>L2</operator_names>
        <![CDATA[
          L2 = rcomplex(0,-kx*kx*0.5);
        ]]>
      </k_operators>
      <![CDATA[
        dphi_dt = L2[phi]*hbar*hbar/m   - i*0.5*m*w*w*1.05*x*x*phi   
                  - i*hbar*hbar*0.5/m*2/mygamma*( 2*mod2(phi) 
                  - 2/mygamma*( A*C*log( 1/C*mygamma/2*mod2(phi) +1 ) 
                  +  B*D*log( 1/D*mygamma/2*mod2(phi) +1 ) ) )*phi  ;
      ]]>
    </integrate>
  </sequence>

  <output>
    <filename>/var/tmp/breathingMode.xsil</filename>
    <group>
      <sampling>
        <fourier_space> no </fourier_space>
        <lattice>       300 </lattice>
        <moments>pow_dens</moments>
        <![CDATA[
          pow_dens=~phi*phi;
        ]]>
      </sampling>
    </group>
  </output>

</simulation>