Automatic RVP (Resonances Via Pade)

Automatic RVP is a python based code designed to automatically calculate resonances energy and width using a single energy level stabilization graph as input.

The code identifies the flat region of the stabilization graph, calculates the Pade approximant for different sections in that region, and then estimates the corresponding resonance energy and width from each Pade approximant. Later, the code uses a data clustering algorithm to evaluate the mean value of the resonance energy and width based on the results collected.

The final output of the code is the mean resonance energy and width alongside information on the clustering result, and statistical data such as standard deviations. Yet, the code also provides the following data:

1. The stable region found.
2. The resonance energy and width from each Pade approximant.
3. The input data for the clustering algorithm.

Therefore, the code is also modular, and can be broken into 3 different segments, that may run individually, as follows:

1. Stabilization - Identifies a flat region in a stabilization graph.
2. Pade - Calculates Pade approximant for different sections in an input and estimates the corresponding resonance energy and width from each Pade approximant.
3. Clustering - Finds a cluster of resonance energy and width based on an input data.

Installation

# Using pip
pip install automatic-rvp

Usage example

The examples below are short usage examples with default parameters. More detailed examples with inputs and outputs can be found in the example folder. Additionally, a list of available parameters can be found in the wiki.

Automatic resonance position and width

Save a single energy level stabilization data in a txt file ('file_name.txt'). In this file, create two columns separated by tab or space. Save the alpha values in the first column, and the corresponding energy values in the second column (see example input file in the example folder).

Calculate resonance energy and width using :

from rvp import auto_rvp

auto_rvp(input_file='file_name.txt')

Stable region identification

Save a single energy level stabilization data in a txt file ('file_name.txt'). In this file, create two columns separated by tab or space. Save the alpha values in the first column, and the corresponding energy values in the second column (see example input file in the example folder).

Identify the stable region using:

from stabilization import run_stabilization

run_stabilization(input_file='file_name.txt')

Pade approximant for different sections in an input

Save selected data in a txt file ('file_name.txt'). In this file, create two columns separated by tab or space. Save the alpha values in the first column, and the corresponding energy values in the second column (see example input file in the example folder).

Calculate Pade approximant for different sections in the input file and estimate the corresponding resonance energy and width from each Pade approximant using:

from pade import run_pade

run_pade(input_file='file_name.txt')

Resonance energy and width clusterization

Save a selected data in a csv file ('file_name.csv'). In this file, create five columns separated by commas. Save the real energy values of the resonance in the first column, the imaginary energy values in the second column, the corresponding alpha values in the third column, the corresponding theta values in the fourth column and the corresponding error values in the fifth column (see example input file in the example folder).

Find a cluster of resonance energy and width using:

from clustering import run_clustering

run_clustering(input_file='file_name')

Release History

• 1.0.3
• 1.0.0
  • First version

References

This project is based on Non-Hermitian quantum mechanics theory described in: Moiseyev, N. Non-Hermitian Quantum Mechanics; Cambridge University Press: Cambridge, U.K., 2011.

The RVP method itself is explained in details in: Landau, A., Haritan, I., Kapralova-Zdanska, P. R., & Moiseyev, N. (2016). Atomic and molecular complex resonances from real eigenvalues using standard (hermitian) electronic structure calculations. The Journal of Physical Chemistry A, 120(19), 3098-3108.

About & License

Idan Haritan – idan.haritan@gmail.com

Yochai Safrai - yochai.safrai@gmail.com

https://github.com/haritan/Automatic-RVP

This project is licensed under the GPL v3.0 License - see the LICENSE file for details.