# TDFunctions

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#### TDFunctions

Section Time-Dependent
Type block

This block specifies the shape of a "time-dependent function", such as the envelope needed when using the TDExternalFields block. Each line in the block specifies one function. The first element of each line will be a string that defines the name of the function. The second element specifies which type of function we are using; in the following we provide an example for each of the possible types:

Options:

• tdf_cw:
%TDFunctions
"function-name" | tdf_cw | amplitude
%

The function is just a constant of value amplitude: $f(t)$ = amplitude

• tdf_gaussian:
%TDFunctions
"function-name" | tdf_gaussian | amplitude | tau0 | t0
%

The function is a Gaussian, $f(t) = F_0 \exp( - (t-t_0)^2/(2\tau_0^2) )$, where $F_0$ = amplitude.

• tdf_cosinoidal:
%TDFunctions
"function-name" | tdf_cosinoidal | amplitude | tau0 | t0
%

$f(t) = F_0 \cos( \frac{\pi}{2} \frac{t-2\tau_0-t_0}{\tau0} )$

If $| t - t_0 | > \tau_0$, then $f(t) = 0$.

• tdf_trapezoidal:
%TDFunctions
"function-name" | tdf_trapezoidal | amplitude | tau0 | t0 | tau1
%

This function is a trapezoidal centered around t0. The shape is determined by tau0 and tau1. The function ramps linearly for tau1 time units, stays constant for tau0 time units, and then decays to zero linearly again for tau1 time units.

• tdf_from_file:
%TDFunctions
"function-name" | tdf_from_file | "filename"
%

The temporal shape of the function is contained in a file called filename. This file should contain three columns: first column is time, second and third column are the real part and the imaginary part of the temporal function f(t).

• tdf_from_expr:
%TDFunctions
"function-name" | tdf_from_expr | "expression"
%

The temporal shape of the field is given as an expression (e.g., cos(2.0*t). The letter t means time, obviously. The expression is used to construct the function f that defines the field.

Source information

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