Symbols and Notation๏
Symbol |
Description |
\(\alpha, \beta, \gamma, \ldots\) |
atom types |
\(j, k, l, \ldots\) |
atom indices |
\(b_{\mathrm{coh},\alpha}\) |
the coherent scattering length of atom-types \(\alpha\) |
\(b_{\mathrm{coh},\alpha}^{\dagger}\) |
the complex conjugate of the coherent scattering length of atom-types \(\alpha\) |
\(b_{\mathrm{inc},\alpha}^{2}\) |
the squared incoherent scattering length of atom-types \(\alpha\) |
\(c_{\alpha}\) |
concentration of atom-type \(\alpha\) where \(c_{\alpha} = N_{\alpha} / N\) |
\(C_{\mathbf{vv}jj}(t)\) |
the velocity autocorrelation function of particle \(j\) |
\(C_{\mathbf{vv}jj}(\omega)\) |
the Fourier transform of \(C_{\mathbf{vv}jj}(t)\) |
\(D\) |
diffusion constant |
\(\mathrm{DOS}(\omega)\) |
density of states |
\(\Delta_{j}^2(t)\) |
mean squared displacement of particle \(j\) |
\(E\) |
energy |
\(\mathrm{EISF}(\mathbf{q})\) |
elastic incoherent structure factor |
\(F(\mathbf{q}, t)\) |
intermediate scattering function |
\(F_{\mathrm{coh}}(\mathbf{q}, t)\) |
coherent intermediate scattering function |
\(F_{\mathrm{inc}}(\mathbf{q}, t)\) |
incoherent intermediate scattering function |
\(F_{\mathrm{inc}}^{\text{G}}(\mathbf{q}, t)\) |
Gaussian approximation of the incoherent intermediate scattering function |
\(J_{\mu\nu}(\mathbf{q}, t)\) |
the current correlation function between the currents in the cartesian directions \(\mu\) and \(\nu\) |
\(J_{\mu\nu}(\mathbf{q}, \omega)\) |
the Fourier transform of \(J_{\mu\nu}(\mathbf{q}, t)\) |
\(J^{\mathrm{L}}(\mathbf{q}, t)\) |
the longitudinal current correlation function |
\(J^{\mathrm{L}}(\mathbf{q}, \omega)\) |
the Fourier transform of \(J^{\mathrm{L}}(\mathbf{q}, t)\) |
\(J^{\mathrm{T}}(\mathbf{q}, t)\) |
the transverse current correlation function |
\(J^{\mathrm{T}}(\mathbf{q}, \omega)\) |
the Fourier transform of \(J^{\mathrm{T}}(\mathbf{q}, t)\) |
\(k_{\mathrm{i}}\) |
the wavenumber of the incident neutron |
\(k_{\mathrm{f}}\) |
the wavenumber of the scattered neutron |
\(g(\mathbf{r})\) |
pair distribution function |
\(G(\mathbf{r}, t)\) |
the van Hove function |
\(G^{\mathrm{d}}(\mathbf{r}, t)\) |
distinct part of the van Hove function |
\(G^{\mathrm{s}}(\mathbf{r}, t)\) |
self part of the van Hove function |
\(t\) |
time |
\(t_{\mathrm{cor}}\) |
the total time of the correlation function |
\(t_{\mathrm{tot}}\) |
the total time of the MD simulation |
\(\Delta t\) |
the MD time step |
\(S(\mathbf{q})\) |
static structure factor |
\(S(\mathbf{q}, \omega)\) |
dynamic structure factor |
\(S_{\mathrm{coh}}(\mathbf{q}, \omega)\) |
dynamic coherent structure factor |
\(S_{\mathrm{inc}}(\mathbf{q}, \omega)\) |
dynamic incoherent structure factor |
\(S_{\mathrm{inc}}^{\text{G}}(\mathbf{q}, \omega)\) |
Gaussian approximation of the dynamic incoherent structure factor |
\(T\) |
temperature |
\(m_{\mathrm{n}}\) |
neutron mass |
\(n_{\mathrm{c}}\) |
total number of time steps calculated for the correlation function |
\(n_{\mathrm{t}}\) |
total number of time steps in the MD simulation |
\(N\) |
total number of atoms in the unit cell, simulation or volume \(V\) |
\(N_\alpha\) |
number of atom of type \(\alpha\) |
\(\rho\) |
density |
\(r\) |
distance |
\(\mathbf{r}(t)\) |
the position of an atom at time \(t\) |
\(q\) |
wavenumber |
\(\mathbf{q}\) |
wavevector |
\(\hat{\mathbf{q}}\) |
a unit wavevector along \(\mathbf{q}\) |
\(\mathbf{v}(t)\) |
the velocity of an atom at time \(t\) |
\(W_\alpha\) |
weighting factor for atom-type \(\alpha\) |
\(W_{\alpha\beta}\) |
weighting factor for atom-type pair \(\alpha\beta\) |
\(w_\alpha\) |
individual weight for atom-type \(\alpha\) |
\(\omega\) |
angular frequency |
\(\Delta \omega\) |
the frequency step |