# Semiclassical initial value series solution of the spin boson problem

## Abstract

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom.

- Authors:

- Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth (Israel)

- Publication Date:

- OSTI Identifier:
- 20991254

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 126; Journal Issue: 16; Other Information: DOI: 10.1063/1.2714520; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; CONVERGENCE; CORRELATION FUNCTIONS; DEGREES OF FREEDOM; MONTE CARLO METHOD; NUMERICAL SOLUTION; SEMICLASSICAL APPROXIMATION; SPIN

### Citation Formats

```
Martin-Fierro, Eva, and Pollak, Eli.
```*Semiclassical initial value series solution of the spin boson problem*. United States: N. p., 2007.
Web. doi:10.1063/1.2714520.

```
Martin-Fierro, Eva, & Pollak, Eli.
```*Semiclassical initial value series solution of the spin boson problem*. United States. doi:10.1063/1.2714520.

```
Martin-Fierro, Eva, and Pollak, Eli. Sat .
"Semiclassical initial value series solution of the spin boson problem". United States.
doi:10.1063/1.2714520.
```

```
@article{osti_20991254,
```

title = {Semiclassical initial value series solution of the spin boson problem},

author = {Martin-Fierro, Eva and Pollak, Eli},

abstractNote = {A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom.},

doi = {10.1063/1.2714520},

journal = {Journal of Chemical Physics},

number = 16,

volume = 126,

place = {United States},

year = {Sat Apr 28 00:00:00 EDT 2007},

month = {Sat Apr 28 00:00:00 EDT 2007}

}