Difference between revisions of "Eigenfields.m"
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==Arguments== | ==Arguments== | ||
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| − | + | Hz - field-dependent part of the laboratory-frame Hamiltonian operator | |
| − | + | in Hilbert space, or commutation superoperator in Liouville space, | |
| − | + | normalised to 1 Tesla | |
| − | + | ||
| − | + | Hc - field-independent part of the laboratory-frame Hamiltonian operator | |
| − | + | in Hilbert space, or commutation superoperator in Liouville space, | |
| − | + | containing couplings and offsets | |
| − | + | ||
| − | + | Hmw - observable operator in Hilbert space, or observable vector in | |
| − | + | Liouville space, without the amplitude prefactor | |
| − | + | ||
| − | + | parameters.window - magnetic-field window, Tesla | |
| − | + | ||
| − | + | parameters.mw_freq - microwave frequency, Hz | |
| − | + | ||
| − | + | parameters.orientation - three Euler angles in radians specifying the | |
| − | + | system orientation | |
| − | + | ||
| − | + | parameters.tm_tol - relative transition moment tolerance | |
| − | + | ||
| − | + | parameters.pp_tol - peak position tolerance in Tesla; this should | |
| − | + | be much smaller than the typical line width | |
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| − | + | parameters.fwhm - transition full width at half maximum, Tesla | |
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==Outputs== | ==Outputs== | ||
| − | + | ||
| − | + | tran.tf - vector of transition fields in Tesla | |
| − | + | ||
| − | + | tran.tm - vector of transition moments | |
| − | + | ||
| + | tran.tw - vector of transition FWHMs in Tesla | ||
| + | |||
| + | tran.pd - vector of energy level population differences | ||
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| + | tran.ti - transition identity array, one row per transition | ||
| + | |||
| + | tran.tj - vector of scaled field-sweep Jacobians | ||
==Notes== | ==Notes== | ||
Revision as of 15:22, 5 June 2026
Computes resonance fields. For a Hamiltonian Hc+b*Hz, returns all magnetic fields b for which the difference between two eigenvalues of Hc+b*Hz is equal to the frequency provided, and the transition moment across the specified operator Hmw is significant.
Syntax
tran=eigenfields(spin_system,parameters,Hz,Hc,Hmw)
Arguments
Hz - field-dependent part of the laboratory-frame Hamiltonian operator
in Hilbert space, or commutation superoperator in Liouville space,
normalised to 1 Tesla
Hc - field-independent part of the laboratory-frame Hamiltonian operator
in Hilbert space, or commutation superoperator in Liouville space,
containing couplings and offsets
Hmw - observable operator in Hilbert space, or observable vector in
Liouville space, without the amplitude prefactor
parameters.window - magnetic-field window, Tesla
parameters.mw_freq - microwave frequency, Hz
parameters.orientation - three Euler angles in radians specifying the
system orientation
parameters.tm_tol - relative transition moment tolerance
parameters.pp_tol - peak position tolerance in Tesla; this should
be much smaller than the typical line width
parameters.fwhm - transition full width at half maximum, Tesla
Outputs
tran.tf - vector of transition fields in Tesla
tran.tm - vector of transition moments
tran.tw - vector of transition FWHMs in Tesla
tran.pd - vector of energy level population differences
tran.ti - transition identity array, one row per transition
tran.tj - vector of scaled field-sweep Jacobians
Notes
In Hilbert space, the very efficient Schweiger-Stoll method is used. In Liouville space, the very general but rather slow generalised eigensolver supplied with Matlab is used.
See also
Version 2.6, authors: Ilya Kuprov
