Python package to parametrise the multi-channel S-matrix using a pade approximation according to the technique presented in "S.A. Rakityansky P.O.G. Ogunbade. S-matrix parametrization as a way of locating quantum resonances and bound states:multichannel case, 2010".
Clone the repository and install with the following commands:
git clone https://github.com/petersbingham/parsmat.git
cd parsmat
python setup.py install
Author packages (these will have their own dependencies):
- pynumwrap
- channelutil
- tisutil (optional)
- stelempy (optional)
There are four main functions calculate_coefficients, get_elastic_Fin_fun, get_elastic_Smat_fun and get_elastic_Qmat_fun. Each of the functions take an channelutil.AsymCalc like object to describe the channels (see channelutil and example below for more details).
There are two types that the ukrmolmatreader is compatible with, standard python types and mpmath types. Python types is the default. To change to mpmath types call the module function use_mpmath_types().
Coefficients are calculated using the following function:
calculate_coefficients(smatdata, asymcalc)
The smatdata, is a dictionary like (eg python dict or a tisutil.dSmat) of S-matrices keyed by energy that will be used as input to the fit routine. It returns alphas and betas.
Once the coefficients have been calculated they can be passed to the following functions for calculation of scattering quantities. All these functions return either an energy function reference or the indicated tisutil like container.
get_elastic_Fin_fun(coeffs, asymcalc) returns tisutil.cFinMatSympypolyk.
get_elastic_Smat_fun(coeffs, asymcalc) returns tisutil.cSmat.
get_elastic_Spmat_fun returns tisutil.cMat
get_elastic_Qmat_fun returns tisutil.cQmat
The following example illustrates. Explanation follows.
import channelutil as cu
import twochanradialwell as tcrw
import parsmat as psm
calc = cu.AsymCalc(cu.hartrees, [0,0])
cSmat = tcrw.get_Smat_fun(1.0,2.0,2.0,calc,1.0)
dSmat = cSmat.discretise(1.,8.,12)
coeffs = psm.calculate_coefficients(dSmat, calc)
cSmat = psm.get_elastic_Smat_fun(coeffs, calc)
dSmat = cSmat.discretise(1.,8.,100)
dSmat.plot()The first code block imports the required dependent python packages. We are using twochanradialwell to provide our example fit data but the user can of course provide their own. The next single single code block prepares the asymptotic calculator, describing the channels of our calculation. We will look at an elastic twochanradialwell, so the second parameter specifies two channels, each with zero angular momentum. The next block of code prepares our demo fit data from the twochanradialwell, the second line here uses the tisutil.dMat interface to create the dictionary of S-matrices. In the final block of code the fit coefficients are calculated and then used to obtain a function reference to a parameterised S-matrix. Finally this fitted S-matrix is plotted using the tisutil.dMat interface.
The reference quoted at the beginning of this document describes a technique to find the poles of the S-matrix by looking for stable roots of the Fin. For this we recommend using the find_roots of the cPolyVal returned from get_elastic_Fin_fun (if tisutil is available) for several numbers of fit points and then using the stelempy package to locate the stable roots (corresponding to the S-matrix poles). Alternatively, the reskit package provides a tool combining all of this functionality.