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GAMMA Tour
(Γ Version 4.0.6)
 

Double Commutators

Here we will illustrate two things. First the ability in GAMMA to visualize matrix representations of operators, superoperators, etc. Second, the way in which user can easily generate such entities, e.g. double commutation superoperators (used in the treatment of relaxation effects.)

Through the course of a simulation it is often handy to have a peek at the various quantities being used in a calculation. Most GAMMA object can be viewed on the screen or sent to an output file using the standard operator <<. For example the following code

           spin_system sys;
           cout << sys << "\n\n";
           matrix mx(3,2,complexi);
           cout << mx << "\n\n";
           
will send the system sys and matrix mx to the screen (or file if cout is replaced by an ostream attached to a writable file.) Here is what might be seen from this
 
 

The same is true for operators, superoperators, spatial tensors, etc. We can also easily make any spin based operator or superoperator. For example, we can make the double commutation superoperator for a three proton system. The code would look something like this:

           spin_system sys(3);		// Three protons by default
           matrix mx(3,2,complexi);
           cout << mx << "\n\n";
           
The following code will print out
       
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