Abstract The most important paradigms in quantum mechanics are probably a twolevel system, a harmonic oscillator and an ideal (infinite) periodic potential. The first two provide a starting point for understanding the phenomena in systems where the spectrum of energy levels is discrete, whereas the last one results in continuous energy bands. Here an attempt is made to study the dynamics of the electrons in a narrow miniband of a semiconductor superlattice under electric and magnetic fields. Semiconductor superlattices are artificial periodic structures, where certain properties like the period and the energy band structure, defined in standard crystals by the nature, can be controlled. Electron dynamics in a single superlattice miniband is interesting both from the viewpoint of fundamental and applied physics. From the fundamental perspective superlattices serve as a model system for a wealth of phenomena resulting from the wavenature of charge carriers. On the other hand, superlattices can potentially be utilized in oscillators and amplifiers operating at THz frequencies. They can, in principle, provide a reasonable THz Bloch gain under dc bias and parametric amplification in the presence of ac pump field. Because of numerous scientific and technological applications in different areas of science and technology, including astrophysics and atmospheric science, biological and medical sciences, and detection of concealed weapons and biosecurity, a construction of compact tunable THz amplifiers and generators that can operate at room temperature is an important – but so far unrealized – task. This thesis focuses on the influence of electric and magnetic fields on small-signal absorption and gain in semiconductor superlattices in the presence of dissipation (scattering). We present several new ideas how the effects arising due to the wave nature of the electrons can be utilized in an operation of THz oscillators and amplifiers. In Papers I–V, we discuss the properties of superlattice sub-THz and THz parametric amplifiers, whereas the Papers VI–IX are devoted to the problem of domain instability in the realization of cw THz Bloch oscillator. In Paper IX we also establish a feasibility of new type of superlattice THz amplifier based on nonlinear cyclotron-like oscillations of the miniband electrons. The ideas presented in the Papers I–IX are supplemented here with a detailed discussion of the physical origin of the effects and more rigorous mathematical derivations of the main equations.

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