https://www.quanty.org/ 2026-11-15T23:54:03+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2026-11-13T18:20:07+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/functions/bspline?rev=1794594007&do=diff BSpline f = InterpolatingFunction.BSpline(x, y, n) makes a B-spline of degree $n$ through the points $(x_i, y_i)$, an interpolating function of type “BSpline”. It is a sum of $N$ B-splines of degree $n$, $$ f(x) = \sum_{j=1}^{N} c_j B_j(x), $$ with the coefficients $c_j$ such that $f(x_i) = y_i$ for all $N$ points. Between two knots $f$ is a polynomial of degree $n$$f$$n - 1$$N$$N$$1 \leq n \leq N - 1$$n$$N$$c_j$$B_j(x)$$n$$n$$n + 1$$n - 1$$n + 1$$x_1$$n + 1$$x_N$$n$$t_{j+n+1} = (x_{j+1} + \dots… text/html 2026-11-13T18:19:23+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/functions/monotoniccspline?rev=1794593963&do=diff HermiteCSpline f = InterpolatingFunction.HermiteCSpline(x, y) or f = InterpolatingFunction.HermiteCSpline(x, y, m) makes a cubic Hermite spline through the points $(x_i, y_i)$, an interpolating function of type “HermiteCSpline”. On every interval $[x_i, x_{i+1}]$ it is the cubic polynomial with the values $y_i$$y_{i+1}$$m_i$$m_{i+1}$$N \geq 2$$N$$N$$(y_{i+1} - y_i)/(x_{i+1} - x_i)$$h^4$interpolatingfunction index text/html 2026-11-13T18:18:46+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/functions/integrate?rev=1794593926&do=diff Integrate I = InterpolatingFunction.Integrate(f) integrates the interpolating function f over its whole interval, I = InterpolatingFunction.Integrate(f, a, b) from $a$ to $b$, $$ I = \int_a^b f(x) \, dx. $$ Input f : an interpolating function.a, b : (optional) Reals, the limits. For $a > b$ the result is $-\int_b^a f(x) dx$. Both limits must lie inside the interval of $1/r$interpolatingfunction index text/html 2026-11-13T18:18:02+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/functions/spline?rev=1794593882&do=diff Spline f = InterpolatingFunction.Spline(x, y) or f = InterpolatingFunction.Spline(x, y, yp1, ypN) makes a cubic spline through the points $(x_i, y_i)$, an interpolating function of type “Spline”. On every interval $[x_i, x_{i+1}]$ it is a cubic polynomial, and the function, its first and its second derivative are continuous. With two arguments the second derivative is 0 at both ends (a natural spline); with four, the slopes at the ends are $= f'(x_1)$$= f'(x_N)$$N \geq 2$$N$$f''^2$$h^4$$h$$f''$$… text/html 2026-11-13T18:16:51+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/start?rev=1794593811&do=diff Interpolating function An interpolating function is a function $f(x)$ of one real variable made from a table of data points $(x_i, y_i)$, $i = 1 \dots N$. It passes through every data point, $f(x_i) = y_i$, and between the points it is a smooth curve, a polynomial of low degree on each interval. Once made, an interpolating function can be evaluated at any $x$$[x_1, x_N]$$f$$f'$$f''$$f$$f'$$n$$f$$f^{(n-1)}$$n$$x = 0, 1, \dots, 10$$[x_i, x_{i+1}]$$f''^2$$f'' = 0$$f'(x_1)$$f'(x_N)$$h^4$$h$$n$$N$$B_… text/html 2026-11-13T18:14:59+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/interpolatingfunction/functions/start?rev=1794593699&do=diff Functions The functions of the InterpolatingFunction library. InterpolatingFunction.Spline(), InterpolatingFunction.HermiteCSpline() and InterpolatingFunction.BSpline() make an interpolating function from a table of data points, InterpolatingFunction.Integrate() integrates one.functions index text/html 2026-11-13T18:11:07+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/?image=documentation%3Alanguage_reference%3Aobjects%3Ainterpolatingfunction%3Ainterpolation_types.png&ns=documentation%3Alanguage_reference%3Aobjects%3Ainterpolatingfunction&rev=1794593467&tab_details=history&media_do=diff&do=media <img src="https://www.quanty.org/_media/documentation/language_reference/objects/interpolatingfunction/interpolation_types.png?w=500&amp;h=500&amp;tok=c10df3" alt="interpolation_types.png" loading="lazy" width="500" height="500" /> text/html 2026-11-13T18:02:42+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/standard_operators/atomic_coulomb_repulsion?rev=1794592962&do=diff Atomic coulomb repulsion NewOperator(“AtomicU”,NF,indices,RadialWavefunctions1,RadialWavefunctions2,options) calculates the full Coulomb interaction operator between all given atomic orbitals. NewOperator(“AtomicU”,NF,indices,RadialWavefunctions1,RadialWavefunctions2,kappas1,kappas2,options) calculates only the interaction between the orbitals in kappas1 and kappas2.$\kappa$$(ab|ab)$$(ab|ba)$standard_operators index text/html 2026-11-13T07:06:55+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/functions/operatorsetonsiteenergy?rev=1794553615&do=diff OperatorSetOnsiteEnergy (available with next release) OperatorSetOnsiteEnergy($O$, $t$, {$i_1,...,i_n$}) takes an Operator $O$, an optional real value $t$ for the trace average and an optional list {$i_1,...,i_n$} of included orbitals, and sets the trace of these orbitals to $t$ divided by the number of orbitals. It furthermore sets any scalar offset of the operator to 0. If no list of indices is given the function includes all orbitals up to the number of fermionic states, and if no value $t$\b… text/html 2026-11-13T07:06:15+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/functions/eigensystem?rev=1794553575&do=diff Eigensystem Eigensystem calculates the eigen-energies and eigen-vectors of an Operator or matrix. The function comes in several flavors. Eigensystem of matrices val, fun = Eigensystem(A) Input A : Square matrix (table of tables) of doubles Output val : Vector (Table of length #A) of doubles representing the eigen values$(H+1)^{\infty} \psi_0$$\psi_0$$S_z$$H$$S_z$$\approx 10\times k_B \times T$$1.49012*10^{-10}$$1.49012*10^{-8}$$1.49012*10^{-6}$functions index text/html 2026-11-13T07:05:13+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/functions/createresonantspectra?rev=1794553513&do=diff CreateResonantSpectra CreateResonantSpectra($O_1$,$O_2$,$O_3$,$O_4$,$\psi$) calculates \begin{equation} \langle \psi | O_3^{\dagger} \frac{1}{(\omega_1 - \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1^{\dagger})} O_4^{\dagger} \frac{1}{(\omega_2 + \mathrm{i} \Gamma_2/2 + E_0^{(2)} - O_2)} O_4\frac{1}{(\omega_1 + \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1)} O_3 | \psi \rangle, \end{equation} with $E_0^{(i)} = \langle \psi | O_i | \psi \rangle$. The spectrum is returned as a spectrum object. Input $O_1$ :… text/html 2026-11-13T07:03:45+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/functions/createfluorescenceyield?rev=1794553425&do=diff CreateFluorescenceYield CreateFluorescenceYield($O_1$,$O_2$,$O_3$,$\psi$) calculates \begin{equation} \langle \psi | O_2^{\dagger} \frac{1}{(\omega - \mathrm{i} \Gamma/2 + E_0 - O_1^{\dagger})} O_3^{\dagger} O_3\frac{1}{(\omega + \mathrm{i} \Gamma/2 + E_0 - O_1)} O_2 | \psi \rangle, \end{equation} with $E_0 = \langle \psi | O_1 | \psi \rangle$. The spectrum is returned as a spectrum object. Please note that fluorescence yield is the expectation value of an Hermitian operator. The returned spect… text/html 2026-11-13T07:03:01+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/functions/readfplobasisfunctions?rev=1794553381&do=diff ReadFPLOBasisFunctions ReadFPLOBasisFunctions(orbitals,file1,file2) reads the files specified by file1 and file2 that contain the wavefunctions obtained from the FPLO DFT calculation and returns interpolating functions corresponding to the names given by orbitals.functions index text/html 2026-11-13T06:54:38+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/calculateselfenergy?rev=1794552878&do=diff CalculateSelfEnergy ResponseFunction.CalculateSelfEnergy($G_0$,$G$) calculates \begin{equation} \Sigma = G_0^{-1} - G^{-1} \end{equation} The difference is ill-conditioned: $G_0$ and $G$ have their poles at different energies, so two large and nearly equal numbers are subtracted, and the result can lose accuracy and come out non-causal. $G_0$$G$$\Sigma$$H_0$$G_0$$H_1$responsefunction index text/html 2026-11-13T06:53:01+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/new?rev=1794552781&do=diff New ResponseFunction.New(Table) creates a new response function object according to the values in Table. Response functions can be of 5 different types (ListOfPoles, Tri, And, Nat, or DoubleTri) and single-valued or matrix-valued. Below 10 examples for creating each of these response functions by hand at some arbitrary values.$\mu=0$$\mu$$-\mu$$A$$B$$G(\omega,\Gamma)$$A$$B$$A$$B$$$ G(\omega,\Gamma) = A_0 + \sum_{i=1}^{n} \frac{B_{i-1}}{\omega + \mathrm{i}\Gamma/2 - a_i} $$$$ G(\omega,\Gamma) = … text/html 2026-11-13T06:51:40+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/reducepoles?rev=1794552700&do=diff ReducePoles Gout = ResponseFunction.ReducePoles(Gin, NPoles) or Gout = ResponseFunction.ReducePoles(Gin, NPolesVal, NPolesCon) reduces the number of poles in $G_{in}$ to $N_{Poles}$ or to $N_{Poles}^{Val} + N_{Poles}^{Con}$ by merging poles close to each other with small spectral weight (residue) (see appendix of $N_{Poles}^{Val}$$N_{Poles}^{Con}$$N$$2N$responsefunction index text/html 2026-11-13T06:49:22+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/start?rev=1794552562&do=diff Response function The ResponseFunction object in Quanty defines (linear) response functions. For Hamiltonian $H$, ground-state $| \psi_0 \rangle$ and a list of transition operators $T_i$ with $i \in [1,n]$ we define the response function $G(\omega,\Gamma)$ as giving an $n$ by $n$ matrix for each value of $\omega$ and $\Gamma$$$ G_{i,j}(\omega,\Gamma) = \left\langle \psi_0 \middle| T^{\dagger}_i \frac{1}{\omega - H + \mathrm{i} \Gamma/2 + E_0} T^{\phantom{\dagger}}_j \middle| \psi_0 \right\rangle… text/html 2026-11-13T06:45:54+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/graphics/functions/plotbands?rev=1794552354&do=diff PlotBands pl = Graphics.PlotBands(kpath, E, C1, ..., Options) plots a band structure as calculated by TightBinding.CalculateBands() and returns a graphics object, which Graphics.ToSVG(pl) turns into an SVG image. The bands are drawn as lines, colored by their character. pl = Graphics.PlotBands(kpath, G, G1, $k$$k$$k$$c \cdot$$+ (1-c) \cdot$$(c_1, c_2, c_3)$$k$$k$$c = A_c(k,\omega) / A(k,\omega)$$\min(1, s A(k,\omega) / A_{\mathrm{ref}})$$s$$A_{\mathrm{ref}}$$k$$10^{-4}$$\pm 1.5$graphics index text/html 2026-11-13T06:42:53+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/start?rev=1794552173&do=diff Objects Besides functions Quanty defines several objects. The objects included are Complex numbers, Operators, Wavefunctions, Spectra, TightBinding definitions, Interpolating functions, Response functions, and Graphics. Each object comes with a small library (with the same name as the object) that defines several functions specific to the object. Objects furthermore can have several methods and or properties.objects index text/html 2026-11-13T06:20:20+00:00 Maurits W. Haverkort (maurits@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/start?rev=1794550820&do=diff Language Reference This section contains a list of all functions implemented in Quanty. We separate the documentation into 3 parts, Constants, Global functions, and Objects. Constants are lists of some useful numbers (electron mass, value of the speed of light, language_reference index