Hybrid quantum-classical dynamics of pure-dephasing systems
- URL: http://arxiv.org/abs/2303.04538v1
- Date: Wed, 8 Mar 2023 12:22:00 GMT
- Title: Hybrid quantum-classical dynamics of pure-dephasing systems
- Authors: Giovanni Manfredi, Antoine Rittaud, Cesare Tronci
- Abstract summary: We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $widehatH(q,p)=H_C(q,p)boldsymbol1+H_I(q,p)widehatsigma_z$.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the interaction dynamics of a classical oscillator and a quantum
two-level system for different pure-dephasing Hamiltonians of the type
$\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehat{\sigma}_z$. This type
of systems represents a severe challenge for popular hybrid quantum-classical
descriptions. For example, in the case of the Ehrenfest model, the classical
density evolution is shown to decouple entirely from the pure-dephasing quantum
dynamics. We focus on a recently proposed hybrid wave equation that is based on
Koopman's wavefunction description of classical mechanics. This model retains
quantum-classical correlations whenever a coupling potential is present. Here,
several benchmark problems are considered and the results are compared with
those arising from fully quantum dynamics. A good agreement is found for a
series of study cases involving harmonic oscillators with linear and quadratic
coupling, as well as time-varying coupling parameters. In all these cases the
classical evolution coincides exactly with the oscillator dynamics resulting
from the fully classical description. In the special case of time-independent
coupling to a classical oscillator with varying frequency, the quantum Bloch
rotation exhibits peculiar features that escape from the hybrid description. In
addition, nonlinear corrections to the harmonic Hamiltonian lead to an overall
growth of decoherence at long times, which is absent in the fully quantum
treatment.
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