Dynamic properties of Lednev's parametric resonance mechanism

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Abstract
This paper presents a further development of the mechanism for the detection of weak magnetic fields proposed by [Lednev (1991): Bioelectromagnetics 12:71–75]. The fraction of excited oscillator states of an unhydrated ion is studied in a dynamic model driven by the predicted (time‐varying) transition probability in the presence of thermal noise and an unspecified excitation mechanism. The main results of Lednev are confirmed. In addition, I conclude that ultraharmonic and ultrasubharmonic resonances may also be observed, provided that the response time of the dynamic system is similar to the period of the oscillating magnetic field. I discuss the time scales involved in the mechanism and present theoretical constraints on these parameters. The crucial requirement for the theory's applicability is that the lifetime of the excited states of the affected ion oscillator exceeds the period of the applied magnetic field. Numerical solutions of the dynamic system are given and are shown to correspond well to theoretical expectations. The main discrepancy between the theories of Lednev and of Blanchard and Blackman [Blanchard and Blackman (1994): Bioelectromagnetics 15:217–238] appears to be due to an inconsistency in the latter paper. The general problem of robust analysis of experimental data is discussed, and I suggest a test of compliance with the Lednev model that is independent of all parameters except for the ratio of oscillating and static field strength (B1/B0) for many resonance conditions and experimental models.