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amplitude apparatus applied field average became superconducting behavior Boltzmann factor closed ring coherence length constant current source corresponding current fluctuations current induced cylinder D. C. transformer decrease density detector tank circuit dewar electronics enters the ring Equation equipartition theorem evaporated experiments external field field coil field sweep film filter flux change flux detector tank flux enters flux linking flux quantization fluxoid conservation free energy Goodkind increase indium inductor jump rate jumps per second linking the ring magnetic field maximum current mean field theory Mumetal normal number of jumps order parameter power dissipation quantization quantum random region resistor Response of flux ring current Sample holder sample lb sapphire tube shielding shown in Figure signal simply connected solenoid superconducting ring sweep rate temperature dependence temperature range thermal noise thermometer transition varnish voltage wave function weak link width zero current