# Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model

## Abstract

We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along–and hops between–diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case of out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.

- Authors:

- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
- School of Chemistry, The Sackler Faculty of Science, Tel Aviv University, Tel Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 22416166

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPARATIVE EVALUATIONS; COUPLING; DEGREES OF FREEDOM; DIAGRAMS; ELECTRIC CONDUCTIVITY; ELECTRONS; IMPURITIES; MANY-BODY PROBLEM; PATH INTEGRALS; PHONONS; POTENTIAL ENERGY; RELAXATION; RENORMALIZATION; SURFACES; THERMAL EQUILIBRIUM

### Citation Formats

```
Dou, Wenjie, Subotnik, Joseph E., and Nitzan, Abraham.
```*Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model*. United States: N. p., 2015.
Web. doi:10.1063/1.4908034.

```
Dou, Wenjie, Subotnik, Joseph E., & Nitzan, Abraham.
```*Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model*. United States. doi:10.1063/1.4908034.

```
Dou, Wenjie, Subotnik, Joseph E., and Nitzan, Abraham. Sat .
"Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model". United States.
doi:10.1063/1.4908034.
```

```
@article{osti_22416166,
```

title = {Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model},

author = {Dou, Wenjie and Subotnik, Joseph E. and Nitzan, Abraham},

abstractNote = {We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along–and hops between–diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case of out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.},

doi = {10.1063/1.4908034},

journal = {Journal of Chemical Physics},

number = 8,

volume = 142,

place = {United States},

year = {Sat Feb 28 00:00:00 EST 2015},

month = {Sat Feb 28 00:00:00 EST 2015}

}