Appendix A: internal tolerances

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

Tolerance	Default value	Cowboy value	Paranoid values	Comment
	1e-10	1e-2 \epsilon	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	Elements of the Liouvillian with absolute values below this threshold are set to zero and dropped from the sparse array.
sys.tols.prop_chop	1e-10	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.krylov_switchover	1e5	The number of non-zeros in the Liouvillian, above which the Krylov propagation method would be used.
sys.tols.zte_tol	1e-24	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	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	The fraction of non-zeros in the state vector, above which the ZTE procedure would be skipped automatically.
sys.tols.path_drop	1e-10	If the absolute value of the coefficient connecting two subspaces is below this threshold, the subspaces are considered disconnected.
sys.tols.subs_drop	1e-10	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.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.irrep_drop	1e-10	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.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