A numerical benchmark of a two-oscillator toy model shows the mean-field and truncated Wigner methods each outperform plain classical evolution, but in complementary parameter regimes tied to classical instability and entanglement.
High-order quantum back-reaction and quantum cosmology with a positive cosmological constant
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abstract
When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.
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Semiclassical Backreaction: A Qualitative Assessment
A numerical benchmark of a two-oscillator toy model shows the mean-field and truncated Wigner methods each outperform plain classical evolution, but in complementary parameter regimes tied to classical instability and entanglement.