https://www.quanty.org/ 2026-04-16T08:34:57+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/basis?rev=1763603121&do=diff Basis In order to do calculations Quanty needs to know the basis set used. Although Quanty is a many body code, the basis set is defined by one particle modes. These are the boxes (basis states) one can place a particle in. The minimal information Quanty needs to define a basis is the number of Ferminonic modes and Bosonic modes. Fermionic modes can be different orbitals with different spins (spin-orbitals) or different lattice sites. We will refer to these as spin- orbitals and when possible in… text/html 2025-11-20T01:45:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/eigen_states?rev=1763603122&do=diff Eigen states For a given operator ($H$) one can calculate the $N_{psi}$ lowest eigenstates with the function “Eigensystem()”. The function “Eigensystem()” uses iterative methods and needs as an input a starting point. This either can be a set of wavefunctions or a set of restrictions. If $N_{psi}$$(H+1)^\infty$$p$$p$ text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/expectation_values?rev=1763603121&do=diff Expectation values Expectation values are calculated as $\langle \psi_i | O | \psi_j \rangle$. For an $n$ electron wave-function this represents the $3n$ dimensional integral over the position coordinates of all electrons: $$ \begin{align} \langle \psi_i | O | \psi_j \rangle = &\int_{r_1} \int_{r_2} ... \int_{r_n} \psi_i^*(\vec{r}_1, \vec{r}_1, ...\vec{r}_n) \\ \nonumber & O(\vec{r}_1, \vec{r}_1, ...\vec{r}_n)\psi_j(\vec{r}_1, \vec{r}_1, ...\vec{r}_n) dr_1 dr_2 ... dr_n \end{align} $$ … text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/fluorescence_yield?rev=1763603121&do=diff Fluorescence yield Fluorescence spectroscopy is a resonant spectroscopy technique whereby one integrates over the outgoing energies: $$ I_{FY} = \frac{\imath}{\pi} \int G^3(\omega_1,\omega_2) d\omega_2 $$ $I_{FY}$ is a real quantity and in that respect different from the response functions ($G^1$ and $G^3$, where the real and imaginary part are related by Kramers Kronig relations). The normalization $\imath/\pi$$G^3$$\omega_2$$\int 1/(\omega_2 - H_2 + \imath \Gamma/2)d\omega_2 = -\imath\pi$$$ \b… text/html 2025-11-20T01:45:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/operators?rev=1763603122&do=diff Operators Operators are defined in second quantization. Any operator can be written as: $$ \begin{eqnarray} \nonumber O = && \alpha^{(0,0)} 1 \\ \nonumber + \sum_i && \alpha^{(1,0)}_i a^{\dagger}_i + \alpha^{(0,1)}_i a_i \\ \nonumber + \sum_{i,j} && \alpha^{(2,0)}_{i,j} a^{\dagger}_ia^{\dagger}_j + \alpha^{(1,1)}_{i,j} a^{\dagger}_ia_j + \alpha^{(0,2)}_{i,j} a_ia_j \\ + \sum_{i,j,k} && ... . \end{eqnarray} $$ In Quanty one can create a creation operator on spin-orbital $0… text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/resonant_spectra?rev=1763603121&do=diff Resonant spectra Resonant spectra are implemented by calculating a third order Green's function or susceptibility ($\chi_3$): $$ \begin{eqnarray} G^3(\omega_1,\omega_2) = \bigg\langle \psi_i \bigg| T_1^{\dagger} \frac{1}{\omega_1 - H_1 - \imath \Gamma/2} T_2^{\dagger} \quad\quad\quad\quad \\ \nonumber \frac{1}{\omega_2 - H_2 + \imath \Gamma/2} T_2 \frac{1}{\omega_1 - H_1 + \imath \Gamma/2} T_1 \bigg | \psi_i \bigg\rangle, \end{eqnarray} $$ For $2p$ core level resonant inelastic x-ray scatterin… text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/spectra?rev=1763603121&do=diff Spectra Spectra are implemented by calculating the Green's function. We calculate the complex energy dependent quantity: $$ G(\omega) = \bigg\langle \psi_i \bigg| T^{\dagger} \frac{1}{\omega - H + \imath \Gamma/2} T \bigg| \psi_i \bigg\rangle, $$ with $T$ and $H$ an operator given in second quantization and $\psi_i$ a many particle wavefunction. -- Creating a spectrum from a starting state psi -- a transition operator T -- and an Hamiltonian H G = CreateSpectra(H,T,psi) $T$ text/html 2025-11-20T01:45:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/start?rev=1763603122&do=diff Basic components The following pages give an introduction to the basic concepts of preforming calculations in Quanty. Index basics index text/html 2025-11-20T01:45:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/basics/wave_functions?rev=1763603121&do=diff Wave functions Wave-functions can be created from a string containing 1's (occupied) and 0's (unoccupied). For each Fermionic spin-orbital on has one bit. For Bosonic modes Quanty reserves 8 bit, i.e. Bosons can have an occupation from 0 to 255. A wave-function resembling a single electron in a $p_x$$m_l=1$$m_l=-1$