| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Out-of-time-order Operators and the Butterfly Effect | Jordan S. Cotler
; Dawei Ding
; Geoffrey R. Penington
; | Date: |
10 Apr 2017 | Abstract: | Out-of-time-order (OTO) operators have recently become popular diagnostics of
quantum chaos in many-body systems. The usual way OTO operators are introduced
is via a quantization of classical Lyapunov growth, which measures the
divergence of classical trajectories in phase space due to the butterfly
effect. However, it is not obvious how exactly the OTO captures the sensitivity
of a quantum system to its initial conditions beyond the classical limit. In
this paper, we analyze sensitivity to initial conditions in the quantum regime
by recasting OTO operators for many-body systems using various formulations of
quantum mechanics. Notably, we utilize the Wigner phase space formulation to
derive an explicit $hbar$-expansion of the OTO to all orders for spatial
degrees of freedom, and a large spin $1/s$-expansion for spin degrees of
freedom. We find in each case that the leading term is exactly the Lyapunov
growth for the classical limit of the system and argue that quantum corrections
cause the OTO operator to saturate at around the scrambling time. These
semiclassical expansions also provide a new way to numerically compute OTO
operators perturbatively by solving a system’s classical equations of motion
and systematically adding quantum corrections. We also express the OTO operator
in terms of propagators and see from a different point of view how the OTO
operator is a quantum generalization of the divergence of classical
trajectories. | Source: | arXiv, 1704.2979 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |