Difference between revisions of "Redfield integral serial.m"

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m (Rename Arguments section heading to Parameters)
(sync with Spinach main f053e432: Nakajima-Zwanzig support, rlx_onshell/rlx_shift)
 
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{{DISPLAYTITLE:redfield_integral_serial.m}} __NOTOC__
 
{{DISPLAYTITLE:redfield_integral_serial.m}} __NOTOC__
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Redfield integral evaluation, the serial path.
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Bloch-Wangsness-Redfield and Nakajima-Zwanzig integral evaluation through the serial path used inside [[relaxation.m]], following the notation of IK's paper (http://dx.doi.org/10.1016/j.jmr.2010.12.004) but replacing the numerical quadrature proposed there with the faster auxiliary matrix method described in http://dx.doi.org/10.1063/1.4928978; this include is used when relaxation.m is not at the top of the parallelisation call stack, while the asynchronous include is used when it is, and it should not be called directly.
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The calling theory block must set rlx_onshell (true selects the back-rotated kernel that reduces to Redfield theory at zero shift, false the resolvent kernel of Nakajima-Zwanzig theory) and rlx_shift (the Laplace evaluation point, Hz); Redfield theory is the on-shell form at zero shift.
  
 
==Syntax==
 
==Syntax==
  
 
     none - this is an include file
 
     none - this is an include file
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==Description==
 
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This include is called from within [[relaxation.m]] and follows the notation used in IK's paper:
 
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    http://dx.doi.org/10.1016/j.jmr.2010.12.004
 
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with the difference that the numerical quadrature method proposed there has been superceded by the much faster auxiliary matrix method described in:
 
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    http://dx.doi.org/10.1063/1.4928978
 
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This include is called when relaxation.m is not at the top of the parallelisation call stack. It uses a simple for loop to calculate the components of the Redfield superoperator. You should not be calling it directly: this is the deep end of ''Spinach'' kernel programming that is open source as a matter of policy, but is ultimately a very technical module.
 
  
 
==Parameters==
 
==Parameters==
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==See also==
 
==See also==
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[[relaxation.m]], [[redfield_integral_async.m]]
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[[relaxation.m]], [[redfield_integral_async.m]], [[autoexec.m]], [[bos_product_table.m]], [[fft_freq_axis.m]], [[fwhm2rlx.m]], [[icm2hz.m]], [[ifft_time_axis.m]], [[intrep.m]], [[istraceless.m]], [[kq2lin.m]], [[kronm.m]], [[lcurve.m]], [[lin2kq.m]], [[min_int_type.m]], [[prune_subgraphs.m]], [[repcols.m]], [[reprows.m]], [[serpentine.m]], [[st_product_table.m]], [[tikhol1n.m]], [[unihash.m]], [[which_subst.m]], [[xyz2hfc.m]], [[Kernel_utilities]]
  
 
''Version 1.10, authors: [[Ilya Kuprov]]''
 
''Version 1.10, authors: [[Ilya Kuprov]]''

Latest revision as of 07:04, 30 August 2026

Bloch-Wangsness-Redfield and Nakajima-Zwanzig integral evaluation through the serial path used inside relaxation.m, following the notation of IK's paper (http://dx.doi.org/10.1016/j.jmr.2010.12.004) but replacing the numerical quadrature proposed there with the faster auxiliary matrix method described in http://dx.doi.org/10.1063/1.4928978; this include is used when relaxation.m is not at the top of the parallelisation call stack, while the asynchronous include is used when it is, and it should not be called directly.

The calling theory block must set rlx_onshell (true selects the back-rotated kernel that reduces to Redfield theory at zero shift, false the resolvent kernel of Nakajima-Zwanzig theory) and rlx_shift (the Laplace evaluation point, Hz); Redfield theory is the on-shell form at zero shift.

Syntax

    none - this is an include file

Parameters

    This include file is not called directly.

Outputs

    This include file has no direct function return values.

See also

relaxation.m, redfield_integral_async.m, autoexec.m, bos_product_table.m, fft_freq_axis.m, fwhm2rlx.m, icm2hz.m, ifft_time_axis.m, intrep.m, istraceless.m, kq2lin.m, kronm.m, lcurve.m, lin2kq.m, min_int_type.m, prune_subgraphs.m, repcols.m, reprows.m, serpentine.m, st_product_table.m, tikhol1n.m, unihash.m, which_subst.m, xyz2hfc.m, Kernel_utilities

Version 1.10, authors: Ilya Kuprov