Appendix A: internal tolerances

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This section contains the names and default values of all internal tolerance parameters in Spinach. Defaults are safe for all intents and purposes. The cowboy switch (intended for quick and dirty calculations) may be enabled by adding 'cowboy' to sys.enable cell array. The paranoia switch (intended for debugging) may be enabled by adding 'paranoia' to sys.enable cell array. Manually specified values override everything.

Tolerance Default value Cowboy value Paranoid value Description
sys.tols.inter_cutoff
1e-10
1e-2
eps()
If the 2-norm of an interaction tensor is below this threshold (in rad/s), the interaction is ignored.
sys.tols.liouv_zero
1e-10
1e-5
eps()
Elements of the Liouvillian with absolute values below this threshold (in rad/s) are set to zero and dropped from the sparse array.
sys.tols.prop_chop
1e-10
1e-8
eps()
If the exponential propagator is generated using a series expansion, the elements of the series terms with absolute values below this threshold are set to zero and dropped from the sparse array.
sys.tols.subs_drop
1e-10
1e-2
eps()
If the 2-norm of the state vector projection into an independently evolving subspace is found to be smaller than this threshold, the subspace is dropped from the simulation.
sys.tols.irrep_drop
1e-10
1e-2
eps()
If the 2-norm of the state vector projection into an irreducible representation of the symmetry group is found to be smaller than this threshold, the irrep is dropped from the simulation.
sys.tols.path_drop
1e-10
1e-2
eps()
If the absolute value of the Liouvillian element (in rad/s) connecting two subspaces is below this threshold, the subspaces are considered disconnected.
sys.tols.zte_tol
1e-24
1e-6
ZTE disabled
In the Zero Track Elimination procedure, any states yielding tracks with infinity-norm below this threshold are dropped from the basis.
sys.tols.zte_nsteps
32
16
ZTE disabled
The number of time steps in the trajectory used to identify zero tracks. The time step is set automatically to the reciprocal 1-norm of the Liouvillian.
sys.tols.zte_maxden
0.5
0.5
ZTE disabled
The fraction of non-zeros in the state vector, above which the Zero Track Elimination procedure would be skipped automatically.
sys.tols.prox_cutoff
100
100
inf()
The distance, in Angstroms, beyond which dipolar interactions are ignored. For simulations that only involve nuclei the appropriate value is 5 Angstrom.
sys.tols.krylov_switchover
100,000
100,000
100,000
The number of non-zeros in the Liouvillian, above which the Krylov propagation method would be used.
sys.tols.basis_hush
256
256
256
If the number of vectors in the basis is above this threshold the full state list is not printed to the log.
sys.tols.merge_dim
16
16
16
If independently evolving subspaces with dimension smaller than this threshold are identified during the trajectory-level state space reduction process, they are bundled together.
sys.tols.small_matrix
200
200
200
If a matrix is found to be smaller than this threshold, dense algebra is used.
sys.tols.dense_matrix
0.15
0.15
0.15
If the fraction of non-zeros in a matrix is found to be greater than this threshold, dense matrix algebra is used.
sys.tols.rlx_integration
1e-4
1e-2
1e-6
Relative accuracy of numerical integration in the evaluation of Redfield superoperator.
sys.tols.dP_method
'auxmat'
'auxmat'
'auxmat'
A switch controlling the selection of the exponential propagator differentiation method.
sys.tols.dd_ncells
2
2
2
Number of periodic boundary condition images on either side of the central cell to be used for the evaluation of dipolar couplings.
sys.tols.cache_mem
7
7
Caching disabled
Number of days days before a cache record is deleted.

The following fundamental constants are built in:

Parameter Value Comment
spin_system.tols.hbar
1.054571628e-34
Planck constant
spin_system.tols.kbol
1.3806503e-23
Boltzmann constant
spin_system.tols.freeg
2.0023193043622
Free electron g-factor
spin_system.tols.mu0
4*pi*1e-7
Vacuum permeability
spin_system.tols.muB
9.274009994e-24
Bohr magneton


Version 1.9, authors: Ilya Kuprov