# Beyond Superconductivity

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## Abstract

We present a novel device concept that utilizes the fascinating transition regime between quantum mechanics and classical physics. The devices operate by using a small number of individual quantum mechanical collapse events to interrupt the unitary evolution of quantum states represented by wave packets. Exceeding the constraints of the unitary evolution of quantum mechanics given by Schrödinger’s equation and of classical Hamiltonian physics, these devices display a surprising behavior.

## Keywords

Superconductivity Maxwell's demon Second law of thermodynamics Nonreciprocal device *Dedicated to Ted Geballe on the occasion of his 100th birthday.*

With his unique enthusiasm, profound understanding, and engaging excitement for venturesome science, Ted has inspired many for decades, certainly including myself. In the friendly sunshine of Santa Barbara’s airport, for example, he suggested to me in his equally sunny style to continue pursuing his and Boris Moyzhes’ ideas of electronic devices designed to convert heat extremely efficiently into electric power [1]. These devices work by utilizing electron motion in a plasma. Fortunately, we took his advice [2].

Now, on the joyful occasion of Ted’s centennial birthday, I am happy to return the favor by presenting him and possible other interested readers with a comparable but even more daring device. Of course, we state that it is even more efficient than his [2]. A secondary aspect which I expect will be of particular interest to him is that such devices open new inroads to large, lossless, normal currents above room temperature—assuming that we are not thoroughly fooled by nature. This caveat obviously applies to my article as a whole.

Before embarking on a description of the device, I note that the specific example presented here is just one of a large family of devices that also include photonic systems [3]. This new concept exploits decoherence or collapse events intermingled with interference processes, as is only possible in the transition range between unitary quantum mechanics and classical physics.

First, we consider electron flow across such a ring in the absence of inelastic scattering. The path lengths along the left or right side of the ring and the magnetic flux reaching through the ring’s hole are chosen such that electrons traveling from contact A to contact B undergo a phase change that differs between the two arms of the ring by 2*nπ*, whereas electrons moving from B to A acquire a phase difference of 2*nπ* + *π*, where *n* is an integer [8, 9].

As a result, electrons moving from A to B zip right through the ring, needing a time *τ*_{A → B}. Electrons traveling from B cannot leave the ring after their first traverse because they would then interfere destructively due to their 2*nπ* + *π* phase differences. These electrons have to fly first forward through the ring, then backward, and then forward again to acquire the phase difference of 2*nπ* + 2*π*, as required for exiting to A.

As a result, the electrons emitted by B linger in the ring three times longer than the electrons from A, *τ*_{B → A} = 3*τ*_{A → B}, which is what Schrödinger’s equation says [10] (and I do not feel thoroughly duped up to now).

Next, we introduce inelastic scattering. We consider the case that the mean inelastic scattering time equals 2*τ*_{A → B} and that the scattering occurs by a deep trapping site. As the electron becomes trapped, it yields its momentum to the substrate’s phonon system. Thereby, the electron loses its momentum, phase, and its respective memories. Thermal fluctuations later release the electron from the trap. Having no information on the original travel direction, the electron travels with nominally equal probability to A or to B. The decoherence associated with trapping prevents the electron motion from being controlled by interference with the original part of the wave function on the opposite arm of the ring (me still feeling undeluded).

Now let us put everything together and place such a trapping site into an arm of the ring (Fig. 1). As *τ*_{B➞A} = 3 *τ*_{A➞B}, the trapping site will catch three times more B➞A than A➞B electrons. But each of the trapped electrons is reemitted to reach A or B with equal probability! The trapping site therefore creates an imbalance by sending back a disproportionately large number of electrons arriving from B.

As a result, these rings let electrons pass preferably in one direction, namely from A to B. If fed by a thermal source in thermal equilibrium, devices of this kind create an imbalance of the electron density between the two contacts. This difference in the electrochemical potential can be used to drive a current through an ohmic resistor, charge a capacitor, or perform work [11] and [12, 13, 14]. As my caveat still applies, however, let us ask nature—much as Ted would do—directly in the lab how she has solved this problem.

Happy Birthday, Ted!

## Notes

### Acknowledgments

The author gratefully acknowledges the valuable contributions of his collaborators D. Braak, P. Bredol, and H. Boschker, as well as helpful discussions with numerous colleagues, in particular T. Kopp.

### Funding Information

Open access funding provided by Max Planck Society.

## References

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## Copyright information

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