Irwin, K. D. (2006). Thermodynamics of nonlinear bolometers near equilibrium. In Proc. 11th International Workshop on Low Temp. Detectors (Vol. 559, pp. 718–720).
Abstract: We present the first thermodynamically correct calculation of the noise in a simple nonlinear resistive bolometer or calorimeter operated out of equilibrium. The solution is rigorous only for first- and second-order deviations from equilibrium, and for the linear and quadratic terms of dissipative elements. In contrast, existing models of noise in resistive bolometers are based on the application of equilibrium theories to a system that is often nonlinear and out of equilibrium. We derive solutions applicable both in and out of steady state. The noise has power spectral density different from the equilibrium theory, and it has higher-order correlations and non-Gaussian characteristics. The results do not apply to non-Markovian hidden variables in the bolometer.
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Gurevich, A. V., & Mints, R. G. (1987). Self-heating in normal metals and superconductors. Rev. Mod. Phys., 59(4), 941–1000.
Abstract: This review is devoted to the physics of current-carrying superconductors and normal metals having two or more stable states sustained by Joule self-heating. The creation, propagation, and localization of electrothermal domains and switching waves leading to the transition from one stable state to another in uniform and nonuniform samples are treated in detail. The connection between thermal bistability and hysteresis, dropping and stepped current-voltage characteristics, self-induced oscillations of current and voltage, selfreplication of electrothermal domains, and the formation of periodic and stochastic resistive structures are considered.
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Tinkham, M., Free, J. U., Lau, C. N., & Markovic, N. (2003). Hysteretic I–V curves of superconducting nanowires. Phys. Rev. B, 68, 134515(1 to 7).
Abstract: Experimental I–V curves of superconducting MoGe nanowires show hysteresis for the thicker wires and none for the thinner wires. A rather quantitative account of these data for representative wires is obtained by numerically solving the one-dimensional heat flow equation to find a self-consistent distribution of temperature and local resistivity along the wire, using the measured linear resistance R(T) as input. This suggests that the retrapping current in the hysteretic I–V curves is primarily determined by heating effects, and not by the dynamics of phase motion in a tilted washboard potential as often assumed. Heating effects and thermal fluctuations from the low-resistance state to a high-resistance, quasinormal regime appear to set independent upper bounds for the switching current.
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Shah, N., Pekker, D., & Goldbart, P. M. (2008). Inherent stochasticity of superconductor-resistor switching behavior in nanowires. Phys. Rev. Lett., 101, 207001(1 to 4).
Abstract: We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.
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Usadel, K. D. (1970). Generalized diffusion equation for superconducting alloys. Phys. Rev. Lett., 25(8), 507.
Abstract: Eilenberger's transportlike equations for a superconductor of type II can be simplified very much in the dirty limit. In this limit a diffusionlike equation is derived which is the generalization of the de Gennes-Maki theory for dirty superconductors to arbitrary values of the order parameter.
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