Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGaussian polymer chains in a harmonic potential: The path integral approach
104
0
0.0
(
0
)
Added by
Georgii Paradezhenko
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We study conformations of the Gaussian polymer chains in d-dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability distribution function of the gyration radius. We calculate this function using Monte Carlo simulations and show that our numerical and theoretical results are in a good agreement for different values of the external field.
rate research
Read More
Many dynamics are random processes with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes path large deviations can be computed from the large interval asymptotic of a certain Fredholm determinant. The latter can be evaluated explicitly using Widoms theorem which generalizes the celebrated Szego-Kac formula to the multi-dimensional case. This provides a large class of dynamics with explicit path large deviation functionals. Inspired by problems in hydrodynamics and atmosphere dynamics, we present the simplest example of the emergence of metastability for such a process.
We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymer, the crossing rate ($mathcal{R}$) monotonically decreases with chain contour length ($L$), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with $L$ but becomes nearly constant for large $L$. For a fixed $L$, the crossing rate becomes maximum at an intermediate bending stiffness. For a self-avoiding chain, the rate is a nonmonotonic function of $L$, first decreasing with $L$, and then, above certain length, increasing with $L$. These findings can be instrumental for efficient separation of biopolymers.
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynmans path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schr{o}dingers formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.
We detail the use of simple machine learning algorithms to determine the critical Bose-Einstein condensation (BEC) critical temperature $T_text{c}$ from ensembles of paths created by path-integral Monte Carlo (PIMC) simulations. We quickly overview critical temperature analysis methods from literature, and then compare the results of simple machine learning algorithm analyses with these prior-published methods for one-component Coulomb Bose gases and liquid $^4$He, showing good agreement.
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schrodinger Equation containing a fractional Laplacian has been proposed. In this work, we develop a Fractional Path Integral Monte Carlo algorithm that can be used to study the finite temperature behavior of the time-independent Fractional Schrodinger Equation for a variety of potentials. In so doing, we derive an analytic form for the finite temperature fractional free particle density matrix and demonstrate how it can be sampled to acquire new sets of particle positions. We employ this algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians. We find that the fractional Laplacian strongly encourages particle delocalization, even in the presence of interactions, suggesting that fractional Hamiltonians may manifest atypical forms of condensation. Our work opens the door to studying fractional Hamiltonians with arbitrarily complex potentials that escape analytical solutions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
