Since "nzero" may be a little confusing, fcs.cpp was modified

so that "nzero" is no longer printed.
Support a new function to print (atomic) participation ratio.
Documents are updated accordingly.

alm/fcs.cpp

@@ -47,8 +47,9 @@ void Fcs::init(){
 
     std::cout << std::endl;
     for (i = 0; i < maxorder; ++i) {
-        std::cout << "  Number of " << std::setw(9) << interaction->str_order[i] << " FCs (nzero): " << ndup[i].size();
-        std::cout << " ( " << nzero[i] << " ) " << std::endl;
+        std::cout << "  Number of " << std::setw(9) << interaction->str_order[i] << " FCs : " << ndup[i].size();
+	std::cout << std::endl;
+	//        std::cout << " ( " << nzero[i] << " ) " << std::endl;
     }
     std::cout << std::endl;
 

anphon/phonon_dos.cpp

@@ -648,7 +648,7 @@ void Dos::calc_scattering_phase_space_with_Bose_mode(const unsigned int nk, cons
     unsigned int i, is, js, k1, k2;
     unsigned int iT;
     unsigned int ns2 = ns * ns;
-    double omega1, omega2;
+    double omega0, omega1, omega2;
     double temp;
     double ret1, ret2;
     double n1, n2, f1, f2;
@@ -665,6 +665,8 @@ void Dos::calc_scattering_phase_space_with_Bose_mode(const unsigned int nk, cons
     for (i = 0; i < nk; ++i) kmap_identity[i] = i;
 
 
+    omega0 = writes->in_kayser(omega);
+
 #pragma omp parallel private(i, is, js, k1, k2, omega1, omega2, energy_tmp, weight)
     {
         memory->allocate(energy_tmp, 2, nk);
@@ -682,18 +684,18 @@ void Dos::calc_scattering_phase_space_with_Bose_mode(const unsigned int nk, cons
                 omega1 = eval[k1][is];
                 omega2 = eval[k2][js];
 
-                energy_tmp[0][k1] = omega1 + omega2;
-                energy_tmp[1][k1] = omega1 - omega2;
+                energy_tmp[0][k1] = writes->in_kayser(omega1 + omega2);
+                energy_tmp[1][k1] = writes->in_kayser(omega1 - omega2);
             }
 
             if (smearing_method == -1) {
                 for (i = 0; i < 2; ++i) {
-                    integration->calc_weight_tetrahedron(nk, kmap_identity, weight[i], energy_tmp[i], omega);
+                    integration->calc_weight_tetrahedron(nk, kmap_identity, weight[i], energy_tmp[i], omega0);
                 }
             } else {
                 for (i = 0; i < 2; ++i) {
                     integration->calc_weight_smearing(nk, nk, kmap_identity, weight[i],
-                        energy_tmp[i], omega, smearing_method);
+                        energy_tmp[i], omega0, smearing_method);
                 }
             }
 

anphon/write_phonons.cpp

@@ -766,10 +766,6 @@ void Writes::write_scattering_amplitude()
     double dT = system->dT;
     unsigned int NT = static_cast<unsigned int>((Tmax - Tmin) / dT) + 1;
 
-    //    static const double factor = std::pow(time_ry, 4) * 1.0e+48;
-    //    static const double factor = 1.0 / std::pow(Ry_to_kayser, 4.0);
-    static const double factor = 1.0 / Ry_to_kayser;
-
     double omega;
 
     ofs_w.open(file_w.c_str(), std::ios::out);
@@ -797,8 +793,8 @@ void Writes::write_scattering_amplitude()
             for (j = 0; j < NT; ++j) {
                 ofs_w << std::setw(5) << i + 1 << std::setw(5) << is + 1 << std::setw(15) << omega;
                 ofs_w << std::setw(8) << Tmin + static_cast<double>(j) * dT;
-                ofs_w << std::setw(15) << dos->sps3_with_bose[i][is][j][1] * factor;
-                ofs_w << std::setw(15) << dos->sps3_with_bose[i][is][j][0] * factor;
+                ofs_w << std::setw(15) << dos->sps3_with_bose[i][is][j][1];
+                ofs_w << std::setw(15) << dos->sps3_with_bose[i][is][j][0];
                 ofs_w << std::endl;
             }
             ofs_w << std::endl;

docs/source/formalism/formalism_anphon.rst

@@ -157,6 +157,27 @@ In addition, ``TDOS``-tag is available to compute the two-phonon DOS defined by
 where :math:`\boldsymbol{G}` is a reciprocal lattice vector. The sign :math:`\pm` correspond to absorption and emission processes, respectively. Please note that the computation of the two-phonon DOS can be expensive
 especially when :math:`N_{q}` or :math:`N_{\kappa}` is large.
 
+
+(Atomic) participation ratio
+----------------------------
+
+Participation ratio (PR) and atomic participation ratio (APR) defined in the following may be useful to analyze the localized nature of the phonon mode :math:`\boldsymbol{q}j`.
+
+* Participation ratio (PR)
+
+.. math::
+
+    PR_{\boldsymbol{q}j} = \left(\sum_{\kappa}^{N_{\kappa}} \frac{|\boldsymbol{e}(\kappa;\boldsymbol{q}j)|^{2}}{M_{\kappa}}\right)^{2} \Bigg/
+    N_{\kappa} \sum_{\kappa}^{N_{\kappa}} \frac{|\boldsymbol{e}(\kappa;\boldsymbol{q}j)|^{4}}{M_{\kappa}^{2}}
+
+* Atomic participation ratio (APR)
+
+.. math::
+
+    APR_{\boldsymbol{q}j,\kappa} = \frac{|\boldsymbol{e}(\kappa;\boldsymbol{q}j)|^{2}}{M_{\kappa}} \Bigg/ \left(  N_{\kappa} \sum_{\kappa}^{N_{\kappa}} \frac{|\boldsymbol{e}(\kappa;\boldsymbol{q}j)|^{4}}{M_{\kappa}^{2}} \right)^{1/2}
+
+For an extended eigenmode, the PR value is of order 1, whereas for a localized eigenmodes PR is of order :math:`1/N_{\kappa}` [3]_. APR is an atomic decomposition of PR that satisfies :math:`PR_{\boldsymbol{q}j} = \sum_{\kappa} (APR_{\boldsymbol{q}j,\kappa})^{2}`. To print the PR and APR, please set ``MODE = phonons`` and ``PRINTPR = 1`` in the ``&analysis`` entry field. 
+
 Scattering phase space
 -----------------------
 
@@ -201,7 +222,7 @@ which is given by
      &= \sum_{\ell^{\prime\prime},\kappa^{\prime\prime},\lambda}\Phi_{\mu\nu\lambda}(\ell\kappa;\ell^{\prime}\kappa^{\prime};\ell^{\prime\prime}\kappa^{\prime\prime})r_{\lambda}(\ell^{\prime\prime}\kappa^{\prime\prime}).
     \end{align}
 
-Please set ``GRUNEISEN = 1`` and give an appropriate ``FCSXML`` file containing cubic IFCs to print Gr|umulaut_u|neisen parameters.
+Please set ``GRUNEISEN = 1`` and give an appropriate ``FCSXML`` file containing cubic IFCs to print Gr\ |umulaut_u|\ neisen parameters.
 
 
 Anharmonic self-energy
@@ -251,7 +272,7 @@ To disable the reduction, please set ``TRISYM = 0``.
 Isotope scattering
 ------------------
 
-The effect of isotope scatterings can be considered by the mass perturbation approach proposed by S. Tamura [3]_ by the ``ISOTOPE``-tag.
+The effect of isotope scatterings can be considered by the mass perturbation approach proposed by S. Tamura [4]_ by the ``ISOTOPE``-tag.
 The corresponding phonon linewidth is given by
 
 .. math::
@@ -316,7 +337,7 @@ such as phonon DOS or energy conservation surface related to three-phonon proces
 enough to avoid unscientific oscillations. Choosing appropriate value for :math:`\epsilon` is not a trivial task
 since it may depend on the phonon structure and the density of :math:`\boldsymbol{q}` points.
 
-To avoid such issues, the program *anphon* employs the tetrahedron method [4]_ by default (``ISMEAR = -1``)
+To avoid such issues, the program *anphon* employs the tetrahedron method [5]_ by default (``ISMEAR = -1``)
 for numerical evaluations of Brillouin zone integration containing :math:`\delta(\omega)`.
 When the tetrahedron method is used, the ``EPSILON``-tag is neglected.
 We recommend to use the tetrahedron method whenever possible, even though it may slightly increase the computational cost.
@@ -327,6 +348,8 @@ We recommend to use the tetrahedron method whenever possible, even though it may
 
 .. [2] Y\. Wang *et al.*, J. Phys.: Condens. Matter **22**, 202201 (2010).
 
-.. [3] S\. -I. Tamura, Phys. Rev. B **27**, 858 (1983).
+.. [3] J\. Hafner and M. Krajci, J. Phys.: Condens. Matter **5**, 2489 (1993).
+
+.. [4] S\. -I. Tamura, Phys. Rev. B **27**, 858 (1983).
 
-.. [4] P\. E. Bl\ |umulaut_o|\ chl, O. Jepsen, and O. K. Andersen, Phys. Rev. B **49**, 1450555 (1994).
+.. [5] P\. E. Bl\ |umulaut_o|\ chl, O. Jepsen, and O. K. Andersen, Phys. Rev. B **49**, 1450555 (1994).

docs/source/input/inputanphon.rst

@@ -397,6 +397,21 @@ The first entry **KPMODE** specifies the types of calculation which is followed
  :Description: This flag is available only when ``KPMODE = phonons`` and *KPMODE* = 2.
 
 
+````
+
+* PRINTPR-tag = 0 | 1
+
+ === ====================================================================================
+  0   Do not compute the (atomic) participation ratio
+  1   Compute participation ratio and atomic participation ratio, which will be 
+      stored in  ``PREFIX``.pr and ``PREFIX``.apr respectively.
+ === ====================================================================================
+
+ :Default: 0
+ :Type: Integer
+ :Description: This flag is available when ``KPMODE = phonons``.
+
+
 ````
 
 * ISOTOPE-tag = 0 | 1

docs/source/output.rst

@@ -60,11 +60,21 @@ Output files of anphon
  Mean-square-displacements of atoms.
  Created when ``MODE = phonons`` with **KPMODE** = 2 and ``PRINTMSD = 1``.
 
- * ``PREFIX``.sps
+* ``PREFIX``.sps
 
  Total and mode-decomposed scattering phase space. 
  Created when ``MODE = phonons`` with **KPMODE** = 2 and ``SPS = 1``.
 
+* ``PREFIX``.pr
+
+ Participation ratio of every phonon modes. 
+ Created when ``MODE = phonons`` and ``PRINTPR = 1``.
+
+* ``PREFIX``.apr
+
+ Atomic participation ratio of every phonon modes. 
+ Created when ``MODE = phonons`` and ``PRINTPR = 1``.
+
 * ``PREFIX``.phvel
 
  Phonon group velocity along given :math:`k` paths.