Abstract-Quantum Hamiltonian daemons: Unitary analogs of combustion engines

Eike P. Thesing, Lukas Gilz, and James R. Anglin

https://journals.aps.org/pre/accepted/b5078RbcQ4d1541b18860c61e17faac00ac4c119a

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom ({steady downconversion}), analogous to the steady transfer of energy in a combustion engine from the high Terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [Gilz, Thesing and Anglin, Phys. Rev. E {94} 042127 (2016)]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes non-trivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through non-adiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.