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Algorithm and Parameters

The algorithm for BlochApp is based on eq:T14, eq:T15, eq:T16, and eq:T17. The evolution of the density matrix can be derived from these four equations. They are coupled, first order differential equations and are readily solved with the Runge--Kutta Four method.[6] The only numerical parameter that is required for this method is a time step. Under Parameters there is a Numerical item which allows the user to change the time step as well as the number of time steps between a datum registration. This later item is helpful on a slow computer or when exact data over a short period of time is not necessary. One can also turn the RWA on or off from this dialog box. The RWA is toggled on in the default configuration.

eq:T14, eq:T15, eq:T16, and eq:T17 have a number of physical constants. Both and are set by the sliders. The rest of the constants are set under the Parameters item in the Atomic dialog box which has fields for , , , and A. There are also check boxes that allow the user to turn these effects on or off in order to speed up the algorithm. Two lifetimes, which are related to the atomic parameters, are displayed below the time output.

The amplitude or frequency of the field may be set equal to various functions of time. These options can be found under the Field item. When any of these items are activated, a check will appear next to it. The status of these items is not saved in the configuration file; so, when loading a file which requires one of these options remember to turn it on. When the nPi Pulse option has been selected, the sliders are disabled and the program begins to run. To enable the sliders the user must click the Sliders item which is disabled at all other times. Two of the selections in this item allow the user to parse functions of time for both the amplitude and frequency of the field. The value of a parsed function is added to whatever value is currently registered on the sliders.

Because Windows is an event--driven operating system, we must tell it how often to execute the numerical algorithm. Under Parameters there is a Speed item which informs Windows how often to run a section of BlochApp. The default setting is 50 ms; however, a lower or higher value may help BlochApp execute better. The optimum value depends on the computer and can be found through experimentation.



next up previous contents index
Next: Simulations Up: About BlochApp Previous: Introduction



Andy Antonelli
Wed May 17 14:34:24 EDT 1995