operator.m
Generates Hilbert space operators and Liouville space superoperators from their human-readable descriptions.
Syntax
A=operator(spin_system,operators,spins,operator_type,format)
Arguments
This function supports three types of calls:
1. If operators is a string and spins is a string
operators='Lz'; spins='13C';
the function returns the sum of the corresponding single-spin operators (Hilbert space) or superoperators (Liouville space) on all spins of that type. Valid labels for operators in this type of call are 'E' (identity), 'Lz', 'Lx', 'Ly', 'L+', 'L-', and 'Tl,m' (irreducible spherical tensor, l and m are integers). Valid labels for spins are standard isotope names as well as 'electrons', 'nuclei' and 'all'.
2. If operators is a string and spins is a vector
operators='Lz'; spins=[1 2 4];
the function returns the sum of all single-spin operators (Hilbert space) or superoperators (Liouville space) for all spins with the specified numbers. Valid labels for operators are the same as in Item 1 above.
3. If operators is a cell array of strings and spins is a cell array of numbers
operators={'Lz','L+'}; spins={1,2};
then a product operator (Hilbert space) or its superoperator (Liouville space) is produced. In the case above, Spinach will generate LzS+ in Hilbert space or its specified superoperator in Liouville space. Valid labels for operators are the same as in Item 1 above.
In Liouville space calculations, operator_type can be set to:
'left' - produces left side product superoperator
'right' - produces right side product superoperator
'comm' - produces commutation superoperator (default)
'acomm' - produces anticommutation superoperator
In Hilbert space calculations operator_type parameter is ignored, and the operator itself is always returned.
The format parameter refers to the format of the output:
'csc' - returns a Matlab sparse matrix
'xyz' - returns a [rows, cols, vals] array
Outputs
A - a CSC sparse (default) or a [rows, cols, vals] repre-
sentation of a spin operator or superoperator.
Examples
1. L+ on spin 3
Lp=operator(spin_system,{'L+'},{3});
2. A sum of Lx on all 15N spins in the system
Lx=operator(spin_system,'Lx','15N');
3. AxBx between spin 2 and spin 5
AxBx=operator(spin_system,{'Lx','Lx'},{2,5});
Operators will be generated in Hilbert space and superoperators in Liouville space.
Notes
WARNING: do not try to obtain product commutation superoperators by multiplying up single-spin commutation superoperators. It is easy to see that
\({{\hat{\hat{O}}}^{2}}=\left[ \hat{O},\left[ \hat{O},\_ \right] \right]\ne \left[ {{{\hat{O}}}^{2}},\_ \right]\)
If you require a commutation superoperator corresponding to a multi-spin operator, use the syntax given in Section 3 above.
See also
unit_state.m, unit_oper.m, mprealloc.m, singlet.m, equilibrium.m, state.m, human2opspec.m
Version 2.8, authors: Ilya Kuprov, Luke Edwards, Dmitry Savostyanov
