Apply Commutation Relations
Overview
The Apply Commutation Relations module provides functions to apply predefined commutation rules to expressions containing infinite-dimensional operators. These functions systematically substitute operators using a given set of commutation relations, ensuring proper simplification and reordering.
apply_substituitions(expr, subs)
This function applies commutation relations (or other substitutions) to the infinite part of an Expression. It iterates over each MulGroup in the Expression and updates the infinite part by applying the given substitution rules until no further changes occur.
Parameters
-
expr(Expression):
The symbolic expression to which the substitutions should be applied. -
subs(dict):
A dictionary mapping expressions to their replacements. This is typically a set of commutation relations.
Returns
Expression:
A new expression with the commutation relations applied.
Example Usage
substitution_rules = {
A*B: C # Example AB = C
}
new_expr = apply_substituitions(old_expr, substitution_rules)
apply_commutation_relations(expr, commutation_relations)
A convenience function that calls apply_substituitions, specifically for applying commutation relations.
Parameters
expr(Expression):
The expression to which commutation relations should be applied.commutation_relations(dict):
A dictionary containing commutator substitutions.
Returns
Expression:
A new expression with commutation relations applied.
Example Usage
commutation_relations = {
A * B - B * A: C # Example commutator
}
new_expr = apply_commutation_relations(old_expr, commutation_relations)
extract_ns(expr, structure)
This function creates the commutation relations for each bosonic subspace needed to extract the number operators of a given expression.
Parameters
expr(Expression):
The expression from which the number operators should be extracted.structure(dict):
A mapping of bosonic subspaces to indices indicated by the number operator.
Returns
- Tuple (
Expression,dict):- The transformed expression with extracted number operators.
- A dictionary containing the commutation relations used for extraction.
License
SymPT is licensed under the MIT License. See the LICENSE file for details.
Citation
If you use SymPT in your research, please cite the following paper:
BibTeX Entry:
@misc{diotallevi2024symptcomprehensivetoolautomating,
title={SymPT: a comprehensive tool for automating effective Hamiltonian derivations},
author={Giovanni Francesco Diotallevi and Leander Reascos and Mónica Benito},
year={2024},
eprint={2412.10240},
archivePrefix={arXiv},
primaryClass={quant-ph},
url={https://arxiv.org/abs/2412.10240},
}
APA Citation:
Diotallevi, G. F., Reascos, L., & Benito, M. (2024). SymPT: a comprehensive tool for automating effective Hamiltonian derivations. arXiv preprint arXiv:2412.10240.
IEEE Citation:
G. F. Diotallevi, L. Reascos, and M. Benito, "SymPT: a comprehensive tool for automating effective Hamiltonian derivations," arXiv preprint arXiv:2412.10240, 2024.