# High-order sampling schemes for path integrals and Gaussian chain simulations of polymers

## Abstract

In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.

- Authors:

- Jülich Supercomputing Centre, Institute for Advanced Simulation, FZ Jülich, Jülich (Germany)
- (Germany)
- Institut für Theoretische Physik, Georg-August Universität, Göttingen (Germany)

- Publication Date:

- OSTI Identifier:
- 22415734

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; CHAINS; CONVERGENCE; CORRECTIONS; INTERFACES; MANY-BODY PROBLEM; PATH INTEGRALS; POLYMERS; QUANTUM SYSTEMS; SAMPLING; SURFACE TENSION

### Citation Formats

```
Müser, Martin H., Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken, and Müller, Marcus.
```*High-order sampling schemes for path integrals and Gaussian chain simulations of polymers*. United States: N. p., 2015.
Web. doi:10.1063/1.4919311.

```
Müser, Martin H., Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken, & Müller, Marcus.
```*High-order sampling schemes for path integrals and Gaussian chain simulations of polymers*. United States. doi:10.1063/1.4919311.

```
Müser, Martin H., Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken, and Müller, Marcus. Thu .
"High-order sampling schemes for path integrals and Gaussian chain simulations of polymers". United States. doi:10.1063/1.4919311.
```

```
@article{osti_22415734,
```

title = {High-order sampling schemes for path integrals and Gaussian chain simulations of polymers},

author = {Müser, Martin H. and Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken and Müller, Marcus},

abstractNote = {In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.},

doi = {10.1063/1.4919311},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 17,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}