Newton's Identity in Finite-Bead Fermionic Partition Function
Abstract
For non-interacting fermions in a harmonic trap, the partition function at any discrete number of imaginary time slices (or beads) and for any choice of short-time propagator admits an exact recursion relation derived directly from the contracted determinant form of the path integral. This finite-bead recursion is distinct from earlier continuum-limit recursions, which do not apply to the discrete time partition functions. By identifying a direct correspondence between this recursion and Newton's identity, application of a closed-form result from the theory of partitions provides an exact expression for the one-dimensional n-fermion finite-bead partition function. From this, the Thermodynamic and Hamiltonian energies and specific heats are analytically calculated for any n, N, τ, and propagator choice.
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BibTeX
@misc{chaudhary2026newtons,
title = {{Newton's Identity in Finite-Bead Fermionic Partition Function}},
author = {A. Chaudhary and J. Valenzuela},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.05442},
eprint = {2606.05442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05442},
}
RIS
TY - UNPB
TI - Newton's Identity in Finite-Bead Fermionic Partition Function
AU - A. Chaudhary
AU - J. Valenzuela
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2606.05442
UR - https://arxiv.org/abs/2606.05442
AB - For non-interacting fermions in a harmonic trap, the partition function at any discrete number of imaginary time slices (or beads) and for any choice of short-time propagator admits an exact recursion relation derived directly from the contracted determinant form of the path integral. This finite-bead recursion is distinct from earlier continuum-limit recursions, which do not apply to the discrete time partition functions. By identifying a direct correspondence between this recursion and Newton's identity, application of a closed-form result from the theory of partitions provides an exact expression for the one-dimensional n-fermion finite-bead partition function. From this, the Thermodynamic and Hamiltonian energies and specific heats are analytically calculated for any n, N, τ, and propagator choice.
ER -