Difference between revisions of "Eigenfields.m"

From Spinach Documentation Wiki
Jump to: navigation, search
(→‎Outputs)
(sync with Spinach main f053e432: add the missing parameters.rspt_order documentation)
 
(12 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{DISPLAYTITLE:eigenfields.m}} __NOTOC__
 
{{DISPLAYTITLE:eigenfields.m}} __NOTOC__
−
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 is significant.
+
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==
 
==Syntax==
  
−
    [tf,tm]=eigenfields(spin_system,parameters,Hc,Hz,Hmw)
 
  
−
==Arguments==
+
    tran=eigenfields(spin_system,parameters,Hz,Hc,Hmw)
  
−
    Hc     - laboratory frame Hamiltonian operator (Hilbert  
+
==Parameters==
−
              space) or commutation superoperator (Liouville
+
 
−
              space, containing all spin-spin couplings, but
+
 
−
              no Zeeman terms
+
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
 
   
 
   
−
     Hz    - laboratory frame Hamiltonian operator (Hilbert
+
parameters.window     - magnetic-field window, Tesla
−
              space) or commutation superoperator (Liouville
 
−
              space, containing only Zeeman terms at 1 Tesla
 
 
   
 
   
−
    Hmw    - microwave irradiation operator, without the am-
+
parameters.mw_freq    - microwave frequency, Hz
−
              plitude prefactor
 
 
   
 
   
−
    parameters.window  - magnet field window, Tesla
+
parameters.orientation - three Euler angles in radians specifying the
 +
                        system orientation
 
   
 
   
−
    parameters.mw_freq  - microwave frequency, Hz
+
parameters.tm_tol      - relative transition moment tolerance
 
   
 
   
−
    parameters.tm_tol  - relative transition moment
+
parameters.pp_tol      - peak position tolerance in Tesla; this should
−
                            tolerance
+
                        be much smaller than the typical line width
 
   
 
   
−
    parameters.pp_tol  - peak position tolerance in Tesla,
+
parameters.fwhm        - transition full width at half maximum, Tesla
−
                            this should be much smaller than
+
−
                            the typical line width
+
parameters.rspt_order  - perturbation theory order to use to account
 +
                        for the off-diagonal part of the Hamiltonian,
 +
                        Inf for exact diagonalisation
  
 
==Outputs==
 
==Outputs==
  
−
    tf     - vector of transition fields in Tesla
+
 
 +
tran.tf - vector of transition fields in Tesla
 
   
 
   
−
    tm     -  vector of transition moments
+
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==
 
==Notes==
−
In Liouville space, a very expensive and barely stable generalised eigensolver supplied with Matlab is used.
+
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==
 
==See also==
−
[[fieldsweep.m]]
+
[[fieldsweep.m]], [[acomm.m]], [[arnoldi.m]], [[atranspose.m]], [[aux_mat.m]], [[binpack.m]], [[cheap_norm.m]], [[cheb_coeff.m]], [[clean_up.m]], [[dirdiff.m]], [[expdrop.m]], [[expmint.m]], [[expmint2.m]], [[fftdiff.m]], [[fourdif.m]], [[fourlap.m]], [[frob_chop.m]], [[gaussfun.m]], [[hdot.m]], [[herm_spline.m]], [[jacobianest.m]], [[keep_rank.m]], [[krondelta.m]], [[kronm_new.m]], [[logfactorial.m]], [[lorentzcon.m]], [[lorentzfun.m]], [[md5_hash.m]], [[mprealloc.m]], [[remncomm.m]], [[remtrace.m]], [[rspert.m]], [[rspt_eig.m]], [[snormpdf.m]], [[svd_shrink.m]], [[tikhoind.m]], [[tikhonov.m]], [[trapdiff.m]], [[unit_oper.m]], [[unit_state.m]], [[vvpert.m]], [[Kernel_utilities]]
−
 
 
  
 
''Version 2.6, authors: [[Ilya Kuprov]]''
 
''Version 2.6, authors: [[Ilya Kuprov]]''

Latest revision as of 09:36, 30 August 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)

Parameters

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

parameters.rspt_order  - perturbation theory order to use to account
                        for the off-diagonal part of the Hamiltonian,
                        Inf for exact diagonalisation

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

fieldsweep.m, acomm.m, arnoldi.m, atranspose.m, aux_mat.m, binpack.m, cheap_norm.m, cheb_coeff.m, clean_up.m, dirdiff.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, fourdif.m, fourlap.m, frob_chop.m, gaussfun.m, hdot.m, herm_spline.m, jacobianest.m, keep_rank.m, krondelta.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, remncomm.m, remtrace.m, rspert.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, tikhonov.m, trapdiff.m, unit_oper.m, unit_state.m, vvpert.m, Kernel_utilities

Version 2.6, authors: Ilya Kuprov