Difference between revisions of "Relaxation.m"

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The relaxation superoperator. All options are set during the call to
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{{DISPLAYTITLE:relaxation.m}}
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create.m function. Syntax:
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Relaxation superoperator.
  
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                R=relaxation(spin_system,euler_angles)
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==Syntax==
  
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where euler_angles should be used for solid state systems in which
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    R=relaxation(spin_system,euler_angles)
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the thermal equilibrium state is orientation-dependent.
 
  
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Further information is available in the following papers:
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==Arguments==
  
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        http://dx.doi.org/10.1016/j.jmr.2010.12.004 (Redfield)
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    euler_angles  - (optional) spin system orientation, for
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        http://dx.doi.org/10.1002/mrc.1242          (Lindblad)
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                    solid state systems at low temperature,
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        http://dx.doi.org/10.1007/s00723-012-0367-0 (Nottingham DNP)
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                    where the thermal equilibrium depends
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        http://dx.doi.org/10.1039/c2cp42897k        (Weizmann DNP)
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                    on the orientation
  
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Note: Nottingham relaxation theory is only applicable to cross effect
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==Outputs==
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DNP systems and Weizmann relaxation theory to solid effect and
 
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cross effect DNP systems.
 
  
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Note: The function has been written for minimal memory footprint and
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    R            - relaxation superoperator
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performs aggressive memory recycling. Relaxation superoperator dimen-
 
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sions in excess of 1,000,000 are in practice feasible.
 
  
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Spinach implements a very general case of Bloch-Redfield-Wangsness relaxation theory, which includes all “difficult” contributions, such as interaction rhombicities, cross-correlations and dynamic frequency shifts. Contributions from all couplings present in the system (including quadrupolar and ZFS) are included. So long as the validity conditions of Redfield theory are satisfied, Spinach is not restricted to high-field systems – the role of H0 can be played, for example, by a large isotropic hyperfine coupling.
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==Notes==
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# A variety of relaxation theories are supported, see the spin system specification section of the online manual.
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# The function has been written for minimal memory footprint and performs aggressive memory recycling. Relaxation superoperator dimensions in excess of 1,000,000 are in practice feasible.
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==See also==
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[[equilibrium.m]], [[thermalize.m]], [[hamiltonian.m]], [[lindbladian.m]]
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''Version 2.2, authors: [[Ilya Kuprov]], [[Luke Edwards]], [[Alexander Karabanov]], [[Walter Kockenberger]]''

Revision as of 10:22, 29 August 2018

Relaxation superoperator.

Syntax

    R=relaxation(spin_system,euler_angles)

Arguments

    euler_angles  - (optional) spin system orientation, for
                    solid state systems at low temperature,
                    where the thermal equilibrium depends
                    on the orientation

Outputs

    R             - relaxation superoperator

Notes

  1. A variety of relaxation theories are supported, see the spin system specification section of the online manual.
  2. The function has been written for minimal memory footprint and performs aggressive memory recycling. Relaxation superoperator dimensions in excess of 1,000,000 are in practice feasible.


See also

equilibrium.m, thermalize.m, hamiltonian.m, lindbladian.m


Version 2.2, authors: Ilya Kuprov, Luke Edwards, Alexander Karabanov, Walter Kockenberger

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