Secret loss of unitarity due to the classical background

Secret loss of unitarity due to the classical background We show that a quantum subsystem can become significantly entangled with a classical background through a process with few or no semiclassical backreactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semiclassical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle each other. Thus, the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Secret loss of unitarity due to the classical background

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Secret loss of unitarity due to the classical background

Abstract

We show that a quantum subsystem can become significantly entangled with a classical background through a process with few or no semiclassical backreactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semiclassical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle each other. Thus, the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.025005
Publisher site
See Article on Publisher Site

Abstract

We show that a quantum subsystem can become significantly entangled with a classical background through a process with few or no semiclassical backreactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semiclassical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle each other. Thus, the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 15, 2017

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