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Merge branch 'bosonic-pimd-langevin' of https://github.com/yotamfe/lammps into bosonic-pimd-langevin

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Ofir Blumer
2025-01-15 10:36:55 +02:00
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1 changed files with 20 additions and 16 deletions
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doc/src/fix_pimdb.rst
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@ -67,7 +67,7 @@ The *pimdb* commands share syntax with the equivalent *pimd* commands. The user
detailed syntax description and additional, general capabilities of the commands.
The major differences from fix *pimd* in terms of capabilities are:
* Fix *pimdb/nvt* the only supports the "pimd" and "nmpimd" methods. Fix *pimdb/langevin* only supports the "pimd" method, and the keyword *method* should not be used. These restrictions are related to the use of normal modes, which change in bosons. For similar reasons, *fmmode* of *pimd/langevin* should not be used, and would raise an error if set to a value other than *physical*.
* Fix *pimdb/nvt* the only supports the "pimd" and "nmpimd" methods. Fix *pimdb/langevin* only supports the "pimd" method, which is the default in this fix. These restrictions are related to the use of normal modes, which change in bosons. For similar reasons, *fmmode* of *pimd/langevin* should not be used, and would raise an error if set to a value other than *physical*.
* Fix *pimdb/langevin* currently does not support *ensemble* other than *nve*, *nvt*. The barostat related keywords *iso*, *aniso*, *barostat*, *taup* are not supported.
@ -84,23 +84,23 @@ distinguishable particles. The sum is over all permutations :math:`\sigma`. Reca
.. math::
E^\sigma = \frac{mP}{2\beta^2 \hbar^2} \sum_{\ell=1}^N \sum_{j=1}^P \left(\bf{r}_\ell^j - \bf{r}_\ell^{j+1}\right)^2,
E^\sigma = \frac{mP}{2\beta^2 \hbar^2} \sum_{\ell=1}^N \sum_{j=1}^P \left(\bf{q}_\ell^j - \bf{q}_\ell^{j+1}\right)^2,
where :math:`P` is the number of beads and :math:`\bf{r}_\ell^{P+1}=\bf{r}_{\sigma(\ell)}^1.`
where :math:`P` is the number of beads and :math:`\bf{q}_\ell^{P+1}=\bf{q}_{\sigma(\ell)}^1.`
Hirshberg et. al. showed that the ring polymer potential
:math:`-\frac{1}{\beta}\textrm{ln}\left[ \frac{1}{N!} \sum_\sigma e ^ { -\beta E^\sigma } \right]`, which scales exponentially with :math:`N`,
can be replaced by a potential :math:`V^{[1,N]}` defined through a recurrence relation :ref:`(Hirshberg) <Hirshberg>`:
can be replaced by a potential :math:`V^{[1,N]}` defined through a recurrence relation :ref:`(Hirshberg1) <Hirshberg>`:
.. math::
e ^ { -\beta V^{[1,N]} } = \frac{1}{N} \sum_{k=1}^N e ^ { -\beta \left( V^{[1,N-k]} + E^{[N-K+1,N} \right)}.
e ^ { -\beta V^{[1,N]} } = \frac{1}{N} \sum_{k=1}^N e ^ { -\beta \left( V^{[1,N-k]} + E^{[N-K+1,N]} \right)}.
Here, :math:`E^{[N-K+1,N]}` is the spring energy of the ring polymer obtained by connecting the beads of particles :math:`N − k + 1, N − k + 2, ..., N` in a cycle.
This potential does not include all :math:`N!` permutations, but samples the same bosonic partition function. The implemented algorithm in LAMMPS for calculating
the potential is the one developed by Feldman and Hirshberg, which scales like :math:`N^2+PN` :ref:`(Feldman) <Feldman>`.
The forces are calculated as weighted averages over the representative permutations,
through an algorithm that scales the same as the one for the potential calculation :math:`N^2+PN` :ref:`(Feldman) <Feldman>`.
through an algorithm that scales the same as the one for the potential calculation, :math:`N^2+PN` :ref:`(Feldman) <Feldman>`.
Restart, fix_modify, output, run start/stop, minimize info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
@ -108,15 +108,15 @@ Restart, fix_modify, output, run start/stop, minimize info
The use of :doc:`binary restart files <restart>` and :doc:`fix_modify <fix_modify>` is the same as in :doc:`fix pimd <fix_pimd>`.
Fix *pimdb/nvt* computes a global 4-vector, which can be accessed by
various :doc:`output commands <Howto_output>`. The three quantities in
various :doc:`output commands <Howto_output>`. The quantities in
the global vector are:
#. the total spring energy of the quasi-beads,
#. the current temperature of the classical system of ring polymers,
#. the current value of the scalar virial estimator for the kinetic
energy of the quantum system :ref:`(Herman) <HermanBB>`.
energy of the quantum system :ref:`(Herman) <HermanBB>` (see the justification in the supporting information of :ref:`(Hirshberg2) <HirshbergInvernizzi>`),
#. the current value of the scalar primitive estimator for the kinetic
energy of the quantum system :ref:`(Hirshberg) <Hirshberg>`.
energy of the quantum system :ref:`(Hirshberg1) <Hirshberg>`.
The vector values calculated by fix *pimdb/nvt* are "extensive", except for the
temperature, which is "intensive".
@ -124,14 +124,14 @@ temperature, which is "intensive".
Fix *pimdb/langevin* computes a global 6-vector, which
can be accessed by various :doc:`output commands <Howto_output>`. The quantities in the global vector are:
#. kinetic energy of the beads
#. spring elastic energy of the beads
#. potential energy of the bead
#. kinetic energy of the beads,
#. spring elastic energy of the beads,
#. potential energy of the bead,
#. total energy of all beads (conserved if *ensemble* is *nve*)
#. primitive kinetic energy estimator :ref:`(Hirshberg) <Hirshberg>`
#. virial energy estimator :ref:`(Herman) <HermanBB>`
#. primitive kinetic energy estimator :ref:`(Hirshberg1) <Hirshberg>`
#. virial energy estimator :ref:`(Herman) <HermanBB>`.
The first 3 are different for different log files, and the others are the same for different log files.
The first three are different for different log files, and the others are the same for different log files.
Restrictions
""""""""""""
@ -156,7 +156,11 @@ The keyword defaults for fix *pimdb/nvt* are method = pimd, fmass = 1.0, sp
.. _Hirshberg:
**(Hirshberg)** B. Hirshberg, V. Rizzi, and M.Parrinello, “Path integral molecular dynamics for bosons,” Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)
**(Hirshberg1)** B. Hirshberg, V. Rizzi, and M. Parrinello, “Path integral molecular dynamics for bosons,” Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)
.. _HirshbergInvernizzi:
**(Hirshberg2)** B. Hirshberg, M. Invernizzi, and M. Parrinello, “Path integral molecular dynamics for fermions: Alleviating the sign problem with the Bogoliubov inequality,” J Chem Phys, 152, 171102 (2020)
.. _Feldman: