# Classical-quantum correspondence and backreaction

## Abstract

We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for analyzing quantum backreaction problems which we illustrate by a toy model in which a rolling particle slows down due to quantum radiation. In conclusion, the dynamics found using the CQC is in excellent agreement with that found using the much more laborious full quantum analysis.

- Authors:

- Publication Date:

- Research Org.:
- Arizona State Univ., Tempe, AZ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1468675

- Alternate Identifier(s):
- OSTI ID: 1503873

- Grant/Contract Number:
- [SC0013605]

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- [Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 6]; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Vachaspati, Tanmay, and Zahariade, George. Classical-quantum correspondence and backreaction. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.065002.
```

```
Vachaspati, Tanmay, & Zahariade, George. Classical-quantum correspondence and backreaction. United States. doi:10.1103/PhysRevD.98.065002.
```

```
Vachaspati, Tanmay, and Zahariade, George. Wed .
"Classical-quantum correspondence and backreaction". United States. doi:10.1103/PhysRevD.98.065002.
```

```
@article{osti_1468675,
```

title = {Classical-quantum correspondence and backreaction},

author = {Vachaspati, Tanmay and Zahariade, George},

abstractNote = {We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for analyzing quantum backreaction problems which we illustrate by a toy model in which a rolling particle slows down due to quantum radiation. In conclusion, the dynamics found using the CQC is in excellent agreement with that found using the much more laborious full quantum analysis.},

doi = {10.1103/PhysRevD.98.065002},

journal = {Physical Review D},

number = [6],

volume = [98],

place = {United States},

year = {2018},

month = {9}

}

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DOI: 10.1103/PhysRevD.98.065002

DOI: 10.1103/PhysRevD.98.065002

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Cited by: 2 works

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Works referenced in this record:

##
An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field

journal, August 1969

- Lewis, H. R.; Riesenfeld, W. B.
- Journal of Mathematical Physics, Vol. 10, Issue 8

##
Adiabatic Invariance in Simple Harmonic Motion

journal, January 1971

- Parker, Leonard
- American Journal of Physics, Vol. 39, Issue 1

##
Class of Exact Invariants for Classical and Quantum Time‐Dependent Harmonic Oscillators

journal, November 1968

- Lewis, H. R.
- Journal of Mathematical Physics, Vol. 9, Issue 11

##
Quantum and classical behavior in interacting bosonic systems

journal, November 2016

- Hertzberg, Mark P.
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 11

##
Observation of incipient black holes and the information loss problem

journal, July 2007

- Vachaspati, Tanmay; Stojkovic, Dejan; Krauss, Lawrence M.
- Physical Review D, Vol. 76, Issue 2

##
Bound states in bottomless potentials

journal, July 2002

- Vachaspati, Tanmay
- Physical Review A, Vol. 66, Issue 1

##
Quantum excitations in time-dependent backgrounds

journal, April 2013

- Kolopanis, Matthew; Vachaspati, Tanmay
- Physical Review D, Vol. 87, Issue 8

##
Quantum backreaction on classical dynamics

journal, June 2017

- Vachaspati, Tanmay
- Physical Review D, Vol. 95, Issue 12

##
Quantum back reaction in scalar QED as an initial-value problem

journal, July 1989

- Cooper, Fred; Mottola, Emil
- Physical Review D, Vol. 40, Issue 2

##
A fast explicit algorithm for the time-dependent Schrödinger equation

journal, January 1991

- Visscher, P. B.
- Computers in Physics, Vol. 5, Issue 6

##
Quantum source of the back reaction on a classical field

journal, July 1995

- Brout, R.; Massar, S.; Parentani, R.
- Physical Review D, Vol. 52, Issue 2

##
Effective theories of coupled classical and quantum variables from decoherent histories: A new approach to the back reaction problem

journal, February 1998

- Halliwell, J. J.
- Physical Review D, Vol. 57, Issue 4

##
Quantum Backreaction on "Classical" Variables

journal, January 1995

- Anderson, Arlen
- Physical Review Letters, Vol. 74, Issue 5