Related papers: Gaussian polymer chains in a harmonic potential: T…
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and…
In this work an approximated path integral model describing the dynamics of a inextensible chain is presented. To this purpose, the nonlinear constraints which enforce the property of inextensibility of the chain are relaxed and are just…
A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be…
We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush…
An explicit expression is derived for the scattering function of a self-avoiding polymer chain in a $d$-dimensional space. The effect of strength of segment interactions on the shape of the scattering function and the radius of gyration of…
In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in the $3D$ space at a range of chain lengths $N$. The…
A formula is derived for stiffness of a polymer chain in terms of the distribution function of end-to-end vectors. This relationship is applied to calculate the stiffness of Gaussian chains (neutral and carrying electric charges at the…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its transpose allows us to show that for a more complicated network,…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with…
It was recently shown that path integral Monte Carlo can be used to directly compute partition functions of Hamiltonians with vibronic coupling [J. Chem. Phys. 148, 194110 (2018)]. While the importance sampling Monte Carlo integration…
The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are…
We develop a new elementary move for simulations of polymer chains in torsion angle space. The method is flexible and easy to implement. Tentative updates are drawn from a (conformation-dependent) Gaussian distribution that favors…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of the both…
The universal density-force relation is analyzed and the correspondent universal amplitude ratio $B_{real}$ is obtained using the massive field theory approach in fixed space dimensions d=3 up to one-loop order. The layer monomer density…
Sharp-momentum transition matrix elements for scattering from a short-range Gaussian potential are computed using a real-time path integral. The computation is based on a numerical implementation of a new interpretation of the path integral…
The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…