# Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

## Abstract

We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

- Authors:

- Departments of Physics and Mathematics, Princeton University, Princeton, New Jersey 08544 (United States)
- Zentrum Mathematik, TU Munich, Boltzmannstr. 3, 85747 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 22093718

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 53; Journal Issue: 9; Other Information: (c) 2012 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; FLUCTUATIONS; GRAPH THEORY; PARTICLES; QUANTUM MECHANICS; RANDOMNESS; RESONANCE; SCHROEDINGER EQUATION; SPECTRA

### Citation Formats

```
Aizenman, Michael, and Warzel, Simone.
```*Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs*. United States: N. p., 2012.
Web. doi:10.1063/1.4714617.

```
Aizenman, Michael, & Warzel, Simone.
```*Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs*. United States. doi:10.1063/1.4714617.

```
Aizenman, Michael, and Warzel, Simone. Sat .
"Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs". United States.
doi:10.1063/1.4714617.
```

```
@article{osti_22093718,
```

title = {Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs},

author = {Aizenman, Michael and Warzel, Simone},

abstractNote = {We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.},

doi = {10.1063/1.4714617},

journal = {Journal of Mathematical Physics},

number = 9,

volume = 53,

place = {United States},

year = {Sat Sep 15 00:00:00 EDT 2012},

month = {Sat Sep 15 00:00:00 EDT 2012}

}

DOI: 10.1063/1.4714617

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