<li>zero or more keyword/value pairs may be appended</li>
<li>keyword = <em>q</em> or <em>mu</em> or <em>p0</em> or <em>v0</em> or <em>e0</em> or <em>tscale</em> or <em>damp</em> or <em>seed</em>or <em>f_max</em> or <em>N_f</em> or <em>eta</em> or <em>beta</em> or <em>T_init</em></li>
</ul>
<pre class="literal-block">
<em>q</em> value = cell mass-like parameter (mass^2/distance^4 units)
<em>mu</em> value = artificial viscosity (mass/distance/time units)
<em>p0</em> value = initial pressure in the shock equations (pressure units)
<em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
<em>e0</em> value = initial total energy (energy units)
<em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
<em>damp</em> value = damping parameter (time units) inverse of friction <i>&gamma;</i>
<em>seed</em> value = random number seed (positive integer)
<em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
<em>N_f</em> value = number of frequency bins (positive integer)
<em>eta</em> value = coupling constant between the shock system and the quantum thermal bath (positive unitless)
<em>beta</em> value = the quantum temperature is updated every beta time steps (positive integer)
<em>T_init</em> value = quantum temperature for the initial state (temperature units)
<p>The fix qbmsst command couples the shock system to a quantum thermal
bath with a rate that is proportional to the change of the total
energy of the shock system, <i>etot</i> - <i>etot</i><sub>0</sub>.
Here <i>etot</i> consists of both the system energy and a thermal
term, see <a class="reference internal" href="#qi"><span class="std std-ref">(Qi)</span></a>, and <i>etot</i><sub>0</sub> = <em>e0</em> is the
initial total energy.</p>
<p>The <em>eta</em> (<i>&eta;</i>) parameter is a unitless coupling constant
between the shock system and the quantum thermal bath. A small <em>eta</em>
value cannot adjust the quantum temperature fast enough during the
temperature ramping period of shock compression while large <em>eta</em>
leads to big temperature oscillation. A value of <em>eta</em> between 0.3 and
1 is usually appropriate for simulating most systems under shock
compression. We observe that different values of <em>eta</em> lead to almost
the same final thermodynamic state behind the shock, as expected.</p>
<p>The quantum temperature is updated every <em>beta</em> (<i>&beta;</i>) steps
with an integration time interval <em>beta</em> times longer than the
simulation time step. In that case, <i>etot</i> is taken as its
average over the past <em>beta</em> steps. The temperature of the quantum
thermal bath <i>T</i><sup>qm</sup> changes dynamically according to
the following equation where &Delta;<i>t</i> is the MD time step and
<i>&gamma;</i> is the friction constant which is equal to the inverse
<li><em>dhugoniot</em> is the departure from the Hugoniot (temperature units).</li>
<li><em>drayleigh</em> is the departure from the Rayleigh line (pressure units).</li>
<li><em>lagrangian_speed</em> is the laboratory-frame Lagrangian speed (particle velocity) of the computational cell (velocity units).</li>
<li><em>lagrangian_position</em> is the computational cell position in the reference frame moving at the shock speed. This is the distance of the computational cell behind the shock front.</li>
<li><em>quantum_temperature</em> is the temperature of the quantum thermal bath <i>T</i><sup>qm</sup>.</li>
</ol>
<p>To print these quantities to the log file with descriptive column
headers, the following LAMMPS commands are suggested. Here the
<a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> energy command is also enabled to allow
the thermo keyword <em>etotal</em> to print the quantity <i>etot</i>. See
also the <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command.</p>
<p>The global scalar under the entry f_fix_id is the quantity of thermo
energy as an extra part of <i>etot</i>. This global scalar and the
vector of 5 quantities can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. It is worth noting that the
temp keyword under the <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command print
the instantaneous classical temperature <i>T</i><sup>cl</sup> as
described in the command <a class="reference internal" href="fix_qtb.html"><span class="doc">fix qtb</span></a>.</p>
</div>
<hr class="docutils" />
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This fix style is part of the USER-QTB package. It is only enabled if
LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>All cell dimensions must be periodic. This fix can not be used with a
triclinic cell. The QBMSST fix has been tested only for the group-ID
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