# Is quantum energy uncertainty underestimated in liquid molecules?

Liquids have the molecular property that the collision frequency (collisions per time) among the molecules is extremely high; it is at the order of picoseconds. Consequently, the Quantum uncertainty between Energy $$\Delta E$$ and the Lifetime of a molecular state $$\Delta t$$

$$\Delta E \Delta t \geq \frac{\hbar}{2}$$

says that the Energy state of liquid molecules cannot be exactly determined. We have a Minimum energy uncertainty of

$$\Delta E = \frac{\hbar}{2 \Delta t} = O(10^{-22})$$

for liquids, it is approximately 10 percent of the average thermal Energy $$kT$$. One can Interpret this as the "Zero Point Energy" when the molecules are bouncing between the nearest neighbors; but after some time this molecule (compared to ideal solids) is able to break free from the Cage formed by ist neighbors.

Will this collisional zero-Point Energy have some effects?

Moreover, Research Claims that many molecular Dynamics simulations with liquids use simply Newtonian mechanics without respecting Things that I described above

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.134207

On a molecular Level, does Energy uncertainty Play a role when we want to calculate how Long a liquid molecule stays in a Cage with it neighbors or other microscopic dynamic properties and trajectories (at room temperature)?

Of Course the de-Broglie wavelength is far smaller than the interparticle distance at room temperature such that the decoherence process is extremely fast, but more recent Research also Claims that for strongly coupled Systems exhibiting high collision frequency, Quantum effects are also relevant. The Quantum Zeno effect is the extreme case of ultra-high collision frequency with other molecules.

Moreover, thermal Energy is at the range of the intermolecular attraction Energy in liquids, would Quantum Energy uncertainty alter the trajectories of molecules from the classically expected path?

Would it make sense to simulate some liquids Quantum-mechanically?

• I am very curious how you decide when to capitalize words. – electronpusher Jun 15 at 1:00