Quantum chaos can appear in quantum one-body as well as many-body systems. We shall discuss features of pairing in both kinds of systems. Pairing is a genuine many-body quantum phenomenon. For finite-sized systems like atomic nuclei, metallic grains, or dilute ultracold atomic quantum gases the superconducting properties fluctuate. Utilizing semiclassical methods we show how the BCS pairing gaps fluctuate and depend on the dynamics (regular or chaotic) of the mean field. If interactions in a generic many-body system are included beyond the mean field approximation, the residual part of the interaction usually implies features resembling quantum chaos, at least for sufficiently high excitation energies. However, if the residual interaction is of pairing type, quantum chaos may be suppressed. We study the quantum properties of a system of a few (up to 16) interacting fermions confined in a two-dimensional harmonic oscillator. The fermions are assumed to interact through attractive and short-range pairing type force. Precursors of quantum chaos are found at moderate pairing strength, while the chaotic properties are reduced for larger pairing strengths.
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