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Register a new userElliptic solid-on-solid models partition function as a single determinant
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Authors
W. Galleas
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In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the models partition function.
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In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $mathcal{E}_{p, gamma}[widehat{mathfrak{gl}_2}]$ as its underlying symmetry algebra. We elaborate on results previously presented by the author and extend our analysis to include continuous families of single determinantal representations for the models partition function. Interestingly, our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function.
We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a ``stem-flower polymer conformation, and the related mechanism of ``zipping during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of $(1+ u)^{-1}$ where $ uapprox 3/5$ is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we study also regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.
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