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Reviews in Mathematical Physics

Some Mathematical Problems Related to Classical-Quantum Interactions

Robert Olkiewicz

Published Aug 1, 1997• 11 citations
Publisher

Abstract

A mathematical model describing the interaction between classical and quantum systems is proposed. The discrete case of a counter as well as the continuous case of the SQUID-tank model are discussed.
DOI
10.1142/s0129055x97000269

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We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel LCLCLC tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the nonperturbative behavior of the ring and the concomitant nonlinear interaction of the ring with this device.
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