Classical behaviours emerge exactly from quantum theory when environmental interactions happen through collisions; a relationship links momentum changes caused by the environment to the Fourier transform of the potential. This determines whether Wigner functions, which reveal quantum effects as negative regions, stay positive or become negative. Violating this inequality guarantees negativity within these functions and sets a lower bound on how quickly a system heats up while behaving classically.

Classical behaviour arises *exactly* from quantum mechanics under specific conditions, previously thought to be merely an approximation. By examining how environmental interactions, specifically collisions, affect a quantum system, scientists derived a relationship between momentum changes and the shape of the external potential influencing the system. The team from The University of Tokyo has demonstrated a scenario where classical behaviour emerges *exactly* from quantum mechanics; previously considered merely an approximation.

They examined how environmental interactions, specifically collisions, affect a quantum system and derived a relationship linking changes in momentum caused by these impacts to the Fourier transform of the external potential influencing it. This mathematical tool breaks down complex shapes into their basic frequency components, much like separating white light with a prism.

A newly-derived inequality guarantees negativity within Wigner functions, a detailed map showing where a tiny object is likely to be and how fast it’s moving, setting a lower bound on heating rates for classically behaving systems. But this set of tools can predict whether nanoparticles trapped using optical tweezers are truly operating under classical rules?

Wigner Function Positivity Defines Classicality via Environmental Interactions

This breakthrough balances momentum jumps imparted by environmental collisions against negative quantum fluctuations within the system’s Wigner function, sidestepping previous limitations requiring either vanishing Planck’s constant or specific timescale restrictions. By deriving a new inequality linking these momentum kicks to the shape of the potential experienced by the particle, they established both necessity and sufficiency for deviations from simple quadratic potentials when generating negativity; this reveals precisely when quantum effects dominate over classical ones.

A levitated nanoparticle calculation showed how much external force is needed to create ‘Wigner negative’ states within an optical tweezer, mapping out conditions for observing genuine quantum effects, the University of Tokyo team further demonstrated this point. Analysis also revealed that current experiments using nanoparticles trapped in optical lattices may already be operating under dynamics where classical descriptions fail.

While establishing precise conditions for classical behaviour arising from collisions with environmental particles, their work remains limited to that specific interaction mechanism; other decoherence processes, like those stemming from diffuse scattering or Van der Waals forces, have not been similarly examined and could yield different results. Acknowledging unexplored decoherence mechanisms such as gas molecule scattering or Van der Waals forces is important, providing initial steps toward understanding how classical physics can emerge exactly from the quantum world via collisions with environmental particles.

The research moves beyond previous limitations requiring either extremely small Planck’s constant values or specific time scales by focusing on the relationship between momentum transfer from impacts and the shape of forces acting upon a particle. Findings establish an inequality relating the distribution of environmental momentum kicks to the Fourier transform of the potential; this may refine our ability to test for non-classical behaviour in systems like levitated nanoparticles.

This research demonstrated that classical evolution laws can arise *exactly* from quantum mechanics when a system experiences collisions with its environment. Using calculations involving a levitated nanoparticle subject to photon recoil and background gas impacts, they determined the external force needed to generate Wigner negative states within optical tweezers. This work suggests current experiments trapping nanoparticles may already be observing dynamics beyond what classical physics can describe.

👉 More information
🗞 Fundamental bound on Wigner negativity generation from environmental collisions
✍️ Isaac Layton, Takahiro Sagawa and Ken Funo (The University of Tokyo)
🧠 ArXiv: https://arxiv.org/abs/2610.32315

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