Density Matrices notes + demo (ePSproc + PEMtk dev.)

30/08/21

In this notebook density matrices are considered & numerical routines demonstrated.

Density Matrices

The general density operator, for a mixture of indepent states \(|\psi_{n} \rangle\), can be defined as (Eqn. 2.8, Blum [1]):

\begin{equation} \hat{\rho}=\sum_{n}W_{n}|\psi_{n}\rangle\langle\psi_{n}| \end{equation}

Where \(W_{n}\) defines the (statistical) weighting of each state \(\psi_{n}\) in the mixture.

For a given basis set, \(|\phi_{m}\rangle\), the states can be expanded and the matrix elements of \(\boldsymbol{\rho}\) defined (Eqns. 2.9 - 2.11, Blum [1]):

\begin{equation} | \psi_{n} \rangle = \sum_{m'} a_{m'}^{(n)}| \phi_{m'}\rangle \end{equation}

\begin{equation} \hat{\rho}=\sum_{n}\sum_{mm'}W_{n}a_{m'}^{(n)}a_{m}^{(n)*}|\phi_{m'}\rangle\langle\phi_{m}| \end{equation}

And the matrix elements - the density matrix - given explicitly as:

\begin{equation} \boldsymbol{\rho}_{i,j}=\langle\phi_{i}|\hat{\rho}|\phi_{j}\rangle=\sum_{n}W_{n}a_{i}^{(n)}a_{j}^{(n)*} \end{equation}

For all pairs of basis states \((i,j)\). This defines the density matrix in the \(\{|\phi_n\rangle\}\) representation (basis space).

The expectation value of an operator \(\hat{Q}\) can then be found as (Eqn. 2.18, Blum [1]):

\begin{eqnarray} \langle \hat{Q}\rangle & = & \sum_{n}\sum_{mm'}W_{n}a_{m'}^{(n)}a_{m}^{(n)*}\langle\phi_{m}|\hat{Q}|\phi_{m'}\rangle\\ & = & \sum_{mm'}\langle\phi_{m'}|\hat{\rho}|\phi_{m}\rangle\langle\phi_{m}|\hat{Q}|\phi_{m'}\rangle\\ & = & \mathrm{tr}(\rho Q) \end{eqnarray}

For basic examples, in terms of \(|J,M\rangle\) states and alignment, see the Quantum Metrology with Photoelectrons notes.

Here, we’ll look at applying the formalism to photoionization, using ePSproc for the numerics…

[1] Blum, K. (2012). Density Matrix Theory and Applications (3rd Editio, Vol. 64). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20561-3

Setup

import sys
import os
from pathlib import Path
import numpy as np
# import epsproc as ep
import xarray as xr

import matplotlib.pyplot as plt

from datetime import datetime as dt
timeString = dt.now()

import epsproc as ep

# Multijob class dev code
from epsproc.classes.multiJob import ePSmultiJob

* sparse not found, sparse matrix forms not available.
* natsort not found, some sorting functions not available.
* pyevtk not found, VTK export not available.

epDemoDataPath = Path(ep.__path__[0]).parent/'data'/'photoionization'/'n2_multiorb'

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

Load test data

# Class dev code
from epsproc.classes.multiJob import ePSmultiJob
from epsproc.classes.base import ePSbase

# Instantiate class object.
# Minimally this needs just the dataPath, if verbose = 1 is set then some useful output will also be printed.
data = ePSbase(epDemoDataPath, verbose = 1)

# ScanFiles() - this will look for data files on the path provided, and read from them.
data.scanFiles()

/home/paul/github/ePSproc/epsproc/IO.py:657: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['E', np.float(parseLineDigits(dumpSeg[3][2])[0]), 'eV'])
/home/paul/github/ePSproc/epsproc/IO.py:662: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['Lmax', np.int(parseLineDigits(dumpSeg[10][2])[0]), ''])
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/github/ePSproc/epsproc/IO.py:657: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['E', np.float(parseLineDigits(dumpSeg[3][2])[0]), 'eV'])
/home/paul/github/ePSproc/epsproc/IO.py:662: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['Lmax', np.int(parseLineDigits(dumpSeg[10][2])[0]), ''])
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
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*** Job orb6 details
Key: orb6
Dir /home/paul/github/ePSproc/data/photoionization/n2_multiorb, 1 file(s).
{   'batch': 'ePS n2, batch n2_1pu_0.1-50.1eV, orbital A2',
    'event': ' N2 A-state (1piu-1)',
    'orbE': -17.09691397835426,
    'orbLabel': '1piu-1'}

*** Job orb5 details
Key: orb5
Dir /home/paul/github/ePSproc/data/photoionization/n2_multiorb, 1 file(s).
{   'batch': 'ePS n2, batch n2_3sg_0.1-50.1eV, orbital A2',
    'event': ' N2 X-state (3sg-1)',
    'orbE': -17.34181645456815,
    'orbLabel': '3sg-1'}

Density matrix functions - demo with photoionization matrix elements

As of ePSproc v1.3.1-dev commit f5e4019, density matrix routines are implemented in :py:func:epsproc.calc.density (functional forms only).

Note this currently requires Holoviews for plotting.

# Import routines
from epsproc.calc import density