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group_by_operators(expr)

The group_by_operators function groups terms in a symbolic Expr with common Operator factors. The function aggregates the coefficients for terms that share the same Operator factors, returning a dictionary where each key is a Mul of Operator objects and each value is the corresponding summed coefficient.

Parameters

  • expr (Expr):
    The symbolic Expr to analyze.

Returns

A dictionary mapping Mul of Operator objects to their aggregated coefficients. Each key represents a unique combination of operators (simplified as necessary), and each value is the total coefficient associated with that operator term after grouping.

Example Usage

Below is an example demonstrating how to use the group_by_operators function:

from sympy import symbols
from sympt import group_by_operators, BosonOp

omega = symbols("omega", real=True)
omega_z = symbols("omega_z", real=True)
a = BosonOp("a")
ad = Dagger(a)

spin = RDBasis("sigma", 2)
s0, sx, sy, sz = spin.basis

H = omega * ad * a + omega * sz + omega_z * sz

# Group the expression by its quantum operator terms
grouped_terms = group_by_operators(H)
display_dict(grouped_terms)
\(a^{\dagger} a : \omega\)

\(\sigma_{z} : \omega + \omega_z\)

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.

References