The Quantum Speed Limit


 

In 2004, the Dutch theorist Jan Zaanen gave this curious phenomenon a name: Planckian dissipation. He asserted that  in a Nature News & Views article that electrons in these materials, and in other exotic states of matter sometimes referred to as “quantum soup,” are all reaching over  a fundamental quantum speed limit on how fast they can dissipate the energy.

“If you’re on a freeway and all the cars are going at the same speed, it’s not because their engines are identical; it’s just because there is a speed limit,” Hartnoll said.

The German physicist Max Planck, who originated , invented  quantum theory in 1900 by inventing  that  the energy is quantized in discrete packets.

To grasp  why electrons  in the strange metals push up against the putative speed limit, theorists want to find  out where it comes from. The best argument traces the speed limit to the uncertainty principle, the famous formula introduced by Werner Heisenberg in 1927 which  puts an upper limit on the amount of certainty that you can have about the world — or, equivalently, on the amount of definiteness of the  world itself possesses. This upper limit is determined by ħ.

Conjured and approximated by Max Planck in 1900 and later put in reduced form by Paul Dirac, ħ highlights up all over quantum theory. Its extremely small value, now known with high precision,  it represents the quantum unit of action, but in addition, as Heisenberg showed, ħ is the quantum unit of uncertainty: an inescapable, base-level fuzziness in nature. The fuzziness appears when you try measuring two things at once: the position and momentum of a particle, for instance, or how much energy it possesses and for how long. In other words, position and momentum cannot both be defined to greater accuracy than ħ; nor can energy and time. The better you know one, the less certain the other.

The hypothesis is that electrons in strange metals might be “dissipating as quickly as they can consistent with that  uncertainty principle,” Hartnoll explained. The electrons possess an amount of energy that’s proportional to the temperature of the strange metal, and dissipation is a process which takes a certain amount of time. Time and energy can’t both be illustrated to arbitrary precision because of these  uncertainty principle, Hartnoll said, so it’s possible that Planckian dissipation arises “when the dissipation time is as fast as it can be.”

It’s only a rough sketch, he admits. He and other theorists want to prove the quantum bound more scrupulously , which might help clarify why hordes of electrons in materials like cuprates so naturally reach it.

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