# Recovery time in quantum dynamics of wave packets

## Abstract

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of the system is established. The recovery time is the longest for the maximal excitation level.

- Authors:

- Russian Academy of Sciences, Voevodskii Institute of Chemical Kinetics and Combustion, Siberian Branch (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22617099

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 124; Journal Issue: 1; Other Information: Copyright (c) 2017 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; ENERGY SPECTRA; EXCITATION; GAUSS FUNCTION; PROBABILITY; QUANTUM MECHANICS; WAVE PACKETS

### Citation Formats

```
Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru.
```*Recovery time in quantum dynamics of wave packets*. United States: N. p., 2017.
Web. doi:10.1134/S1063776116130112.

```
Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru.
```*Recovery time in quantum dynamics of wave packets*. United States. doi:10.1134/S1063776116130112.

```
Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru. Sun .
"Recovery time in quantum dynamics of wave packets". United States.
doi:10.1134/S1063776116130112.
```

```
@article{osti_22617099,
```

title = {Recovery time in quantum dynamics of wave packets},

author = {Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru},

abstractNote = {A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of the system is established. The recovery time is the longest for the maximal excitation level.},

doi = {10.1134/S1063776116130112},

journal = {Journal of Experimental and Theoretical Physics},

number = 1,

volume = 124,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2017},

month = {Sun Jan 15 00:00:00 EST 2017}

}

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