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Running phonon dynamics
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   :hidden: 

   Phonon_dynamics_files

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In this last step, the resulting atomic dynamics are computed, with time taken into consideration. The dynamics are computed under 60000 time-steps. Phonon-phonon evolution are modeled using the below equation. The first portion of the equation models absorption and the latter emission. Delta_t here is infinitesimal (0.0005e-12).


.. image:: EP_Scat_Equation.PNG
   :width: 325px
   :height: 100px
   :align: left

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.. sidebar:: Key (Phonon-Phonon Scattering)

   .. image:: P_Matrix.PNG
        :width: 20%
        :align: right

   Phonon Matrix Element:

   .. image:: P_Occ.PNG
      :width: 15%
      :align: right

   Phonon Occupation Element:

   .. image:: P_Freq.PNG
      :width: 15%
      :align: right

   Phonon Frequency Element:


| For electron-phonon and hole-phonon evolution, 
| the below equation is used. Again, delta_t here 
| is infinitesimal (0.0005e-12).

.. image:: Actual_PP_Scat.PNG
   :width: 325px
   :height: 100px
   :align: left

.. sidebar:: Key (Electron/Hole-Phonon Scattering)

   .. image:: Eph_Matrix.PNG
        :width: 40%
        :align: right

   Electron/Hole-Phonon Matrix Element:

   .. image:: Eph_fermi.PNG
      :width: 15%
      :align: right

   Electron/Hole Occupation Element:

   .. image:: Eph_E.PNG
      :width: 15%
      :align: right

   Electron/Hole Energy Element:

After each time-step, the occupation states each of the particles are recalculated. The phonon occupation state changes due to the cumulative interactions it has with holes and electrons. Each hole and electron changes occupation states based on its temperature. As both particles either lose or gain energy in the process, temperature change can be found based on both particles' specific heat.