Langmuir kinetics and totally asymmetric volume exclusion in linear chains via Fock space formalism
Abstract
Driven-diffusive systems combining spatial exclusion and bulk exchange, such as the totally asymmetric simple exclusion process coupled with Langmuir kinetics (TASEP-LK), serve as foundational models for particle transport in vehicular traffic, conveyor networks, and mesoscopic flow channels. In this work, we employ an exact Doi-Peliti field-theoretic operator formulation in Fock space to evaluate steady-state observables, continuous phase landscapes, and spatial correlations in finite linear chains up to k = 16. By introducing a decomposition in terms of biorthonormal eigenvectors for asymmetric non-Hermitian matrices, the stationary state is calculated directly from the kernel of the quasi-Hamiltonian, completely bypassing the computationally prohibitive complexity of full matrix diagonalization and time-dependent matrix exponentiation. Across distinct rate regimes and global parametric scans, our exact discrete calculations demonstrate that finite-size stochastic fluctuations naturally smear out singular domain walls, producing smooth density profiles and continuous phase crossovers. Finite-size scaling illustrates how local profiles systematically steepen toward the sharp domain wall predicted by continuum field theory as k → ∞. Furthermore, two-point correlation analysis reveals that in slow-kinetics regimes, spatial fluctuations generate strong inter-site cumulants, causing standard mean-field approximations to systematically underestimate joint occupancy probabilities by 50\%. These findings emphasize the necessity of analytical methods for modeling mesoscopic transport systems and short traffic corridors where local stochastic fluctuations and spatial correlations dominate the stationary dynamics.
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BibTeX
@misc{silva2026langmuir,
title = {{Langmuir kinetics and totally asymmetric volume exclusion in linear chains via Fock space formalism}},
author = {Luis D. S. Silva and Arthur M. S. Carvalho and Francisco A. G. Almeida and Gerson C. Duarte-Filho},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07053},
eprint = {2611.07053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07053},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Langmuir kinetics and totally asymmetric volume exclusion in linear chains via Fock space formalism
AU - Luis D. S. Silva
AU - Arthur M. S. Carvalho
AU - Francisco A. G. Almeida
AU - Gerson C. Duarte-Filho
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07053
UR - https://arxiv.org/abs/2611.07053
AB - Driven-diffusive systems combining spatial exclusion and bulk exchange, such as the totally asymmetric simple exclusion process coupled with Langmuir kinetics (TASEP-LK), serve as foundational models for particle transport in vehicular traffic, conveyor networks, and mesoscopic flow channels. In this work, we employ an exact Doi-Peliti field-theoretic operator formulation in Fock space to evaluate steady-state observables, continuous phase landscapes, and spatial correlations in finite linear chains up to k = 16. By introducing a decomposition in terms of biorthonormal eigenvectors for asymmetric non-Hermitian matrices, the stationary state is calculated directly from the kernel of the quasi-Hamiltonian, completely bypassing the computationally prohibitive complexity of full matrix diagonalization and time-dependent matrix exponentiation. Across distinct rate regimes and global parametric scans, our exact discrete calculations demonstrate that finite-size stochastic fluctuations naturally smear out singular domain walls, producing smooth density profiles and continuous phase crossovers. Finite-size scaling illustrates how local profiles systematically steepen toward the sharp domain wall predicted by continuum field theory as k → ∞. Furthermore, two-point correlation analysis reveals that in slow-kinetics regimes, spatial fluctuations generate strong inter-site cumulants, causing standard mean-field approximations to systematically underestimate joint occupancy probabilities by 50\%. These findings emphasize the necessity of analytical methods for modeling mesoscopic transport systems and short traffic corridors where local stochastic fluctuations and spatial correlations dominate the stationary dynamics.
ER -