Warming in complex physical systems, in particular global warming, attracts significant contemporary interest. It is essential, therefore, to understand basic physical mechanisms leading to overheating. It is well known that application of an electric field to conductors heats electric charge carriers. Often an elevated electron temperature describes the result of the heating. This paper demonstrates that an electric field applied to a conductor with discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes dramatically the conductivity of highly mobile two dimensional electrons in a magnetic field, forcing them into a state with a zero differential resistance. Most importantly the results demonstrate that, in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power.

We report measurements of the rectification of microwave radiation ͑0.7-20 GHz͒ at the boundary between two-dimensional electron systems created by a narrow gap split gate on a silicon surface for different temperatures, electron densities, and microwave power. For frequencies above 4 GHz and different temperatures, the rectified voltage V dc as a function of microwave power P can be collapsed onto a single universal curve V dc * = f * ͑P * ͒ using two scaling parameters. The scaled voltage V dc * is a linear function of power P * for small power and proportional to ͑P * ͒ 1/2 at higher power. A theory is developed which attributes the observed voltage to the thermoelectric response associated with local heating by the microwave radiation of adjacent twodimensional electron systems with different densities n 1 and n 2 . Excellent quantitative agreement is obtained between theory and experiment.