Dinâmica de Langmuir e exclusão de volume em cadeias lineares via formalismo do espaço de Fock

Abstract

The totally asymmetric simple exclusion process (TASEP) and Langmuir dynamics (LK) are classically studied via stochastic methods such as mean field approximations or Monte Carlo simulations. In this work, we propose an alternative approach based on mapping the master equation to a Schrödinger-type equation in Fock space, using second quantization operators. This formalism allows an exact description of stochastic dynamics in finite linear chains, capturing fluctuations neglected by traditional methods. We investigate competitive regimes between TASEP and LK that can lead the system to a non-trivial steady state of lattice occupation density, with parameters controlled by input, output, and diffusion rates. Our results reveal the formation of domain walls, separating regions of high and low density, whose location differs from mean field predictions. Statistical signatures in cumulants (mean, variance, skewness, kurtosis) and joint moments (⟨ni , nj ⟩), highlighting amplified fluctuations in central sites when LK exists. Phase transitions in purely TASEP systems, consistent with known results. The numerical implementation, based on the diagonalization of the quasi-Hamiltonian operator (2 k × 2 k for k = 10 sites),highlighted computational challenges inherent to the method. This work not only validates the applicability of Fock space in combined diffusion problems, but also paves the way for studies of systems with non-Markovian interactions or two-dimensional geometries. In addition, our method offers perspectives for biological systems (e.g., ribosome transport with stochastic binding of tRNA) and materials (adsorption of nanoparticles in nanotubes), where spatial exclusion effects and competitive adsorption are critical.