Appendix A: internal tolerances

This section contains the names and default values of all internal tolerance parameters in Spinach. 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.

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.krylov_switchover	1e5	The number of non-zeros in the Liouvillian, above which the Krylov propagation method would be used.
sys.tols.prox_cutoff	4.0	The distance, in Angstroms, beyond which the dipolar interactions are ignored. This parameter must be increased for simulations involving electrons.
sys.tols.basis_hush	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.inter_sym	1e-5	If the 2-norm of the anti-symmetric part of an interaction tensor is smaller than this threshold (in rad/s), the tensor is symmetrised to machine precision.
sys.tols.merge_dim	16	If independently evolving subspaces smaller than this threshold are identified during the trajectory-level state space reduction process, they are bundled together.
sys.tols.small_matrix	200	If a matrix is found to be smaller than this threshold, dense algebra is used.
sys.tols.dense_matrix	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	Relative accuracy of numerical integration in the evaluation of Redfield superoperator.
sys.tols.dP_method	'auxmat'	A switch controlling the selection of the exponential propagator differentiation method.
sys.tols.dd_ncells	2	Number of periodic boundary condition images on either side of the central cell to be used for the evaluation of dipolar couplings.

The following fundamental constants are built in:

Parameter	Value	Comment
spin_system.tols.hbar	1.054571628e-34	Planck constant
pin_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

Version 1.9, authors: Ilya Kuprov