Classical-quantum correspondence for inverted harmonic oscillator
- URL: http://arxiv.org/abs/2211.10078v2
- Date: Tue, 13 Jun 2023 14:23:24 GMT
- Title: Classical-quantum correspondence for inverted harmonic oscillator
- Authors: Shangyun Wang, Songbai Chen and Jiliang Jing
- Abstract summary: Out-of-time-order correlators (OTOCs) which the initial states are located at any position in the IHO system possess the same exponential growth rates (EGRs) as that at the saddle point.
We show that the classical-quantum correspondence in the IHO system not only depends on the initial system photon number, but also on the central positions of the initial states in the phase space.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the classical-quantum correspondence in the inverted harmonic
oscillator (IHO) system. It is shown that the out-of-time-order correlators
(OTOCs) which the initial states are located at any position in the IHO system
possess the same exponential growth rates (EGRs) as that at the saddle point,
and their EGRs are twice the classical lyapunov exponent (CLE) of the saddle
point. Through the time evolution of mean photon number and the OTOCs, we
exhibit that the classical-quantum correspondence in the IHO system not only
depends on the initial system photon number, but also on the central positions
of the initial states in the phase space. Moreover, we use the Husimi Q
function to visualize the quantum wave packets during the OTOCs grow
exponentially.
Related papers
- Quasiclassical theory of out-of-time-ordered correlators [0.0]
Out-of-time correlators (OTOCs) represent observables that provide useful indicators for chaos.
We present a quasiclassical formalism of OTOCs, which is obtained from the semiclassical van Vleck-Gutzwiller propagator.
arXiv Detail & Related papers (2024-10-08T14:11:49Z) - Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution.
We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions.
We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
arXiv Detail & Related papers (2024-05-27T17:40:39Z) - Motivating semiclassical gravity: a classical-quantum approximation for
bipartite quantum systems [0.0]
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems.
In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and the other subsystem evolves quantum mechanically.
arXiv Detail & Related papers (2023-06-01T18:05:33Z) - Quantum chaos in the Dicke model and its variants [0.0]
We calculate the out-of-time-ordered correlator (OTOC) for different variations of the Dicke model in an open quantum system setting.
This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.
arXiv Detail & Related papers (2023-05-24T18:53:33Z) - Classical approach to equilibrium of out-of-time ordered correlators in
mixed systems [0.0]
The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information.
In this work, we show that classical generalized resonances govern the relaxation to equilibrium of the OTOC in the ubiquitous case of a system with mixed dynamics.
arXiv Detail & Related papers (2023-03-11T01:33:26Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - Quantum Lyapunov exponent in dissipative systems [68.8204255655161]
The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems.
We study the interplay between these two processes.
The OTOC decay rate is closely related to the classical Lyapunov.
arXiv Detail & Related papers (2022-11-11T17:06:45Z) - Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model.
The two-mode Dicke model exhibits normal to superradiant quantum phase transition.
We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
arXiv Detail & Related papers (2022-07-08T11:16:29Z) - Out-of-time-order correlator in the quantum Rabi model [62.997667081978825]
We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase.
We show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size.
arXiv Detail & Related papers (2022-01-17T10:56:57Z) - Qubit-photon bound states in topological waveguides with long-range
hoppings [62.997667081978825]
Quantum emitters interacting with photonic band-gap materials lead to the appearance of qubit-photon bound states.
We study the features of the qubit-photon bound states when the emitters couple to the bulk modes in the different phases.
We consider the coupling of emitters to the edge modes appearing in the different topological phases.
arXiv Detail & Related papers (2021-05-26T10:57:21Z) - Out-of-time-order correlator in coupled harmonic oscillators [0.0]
We numerically observe that the thermal OTOC grows exponentially in time.
The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent.
arXiv Detail & Related papers (2020-04-09T06:42:20Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.