We develop the Floquet scattering theory for quantum-mechanical pumping in mesoscopic conductors. The nonequilibrium distribution function, the dc charge, and heat currents are investigated at arbitrary pumping amplitude and frequency. For mesoscopic samples with a discrete spectrum we predict a sign reversal of the pumped current when the pump frequency is equal to the level spacing in the sample. This effect allows us to measure the phase of the transmission coefficient through the mesoscopic sample. We discuss the necessary symmetry conditions (both spatial and temporal) for pumping.

We analyze the time-dependent energy and heat flows in a resonant level coupled to a fermionic continuum. The level is periodically forced with an external power source that supplies energy into the system. Based on the tunneling Hamiltonian approach and scattering theory, we discuss the different contributions to the total energy flux. We then derive the appropriate expression for the dynamical dissipation, in accordance with the fundamental principles of thermodynamics. Remarkably, we find that the dissipated heat can be expressed as a Joule law with a universal resistance that is constant at all times.

We investigate the distribution function, the heat flow, and the noise properties of an adiabatic quantum pump for an arbitrary relation of pump frequency $\omega$ and temperature. To achieve this we start with the scattering matrix approach for ac transport. This approach leads to expressions for the quantities of interest in terms of the sidebands of particles exiting the pump. The sidebands correspond to particles which have gained or lost a modulation quantum $ħ\omega .$ We find that our results for the pump current, the heat flow, and the noise can all be expressed in terms of a parametric emissivity matrix. In particular we find that the current cross correlations of a multiterminal pump are directly related to a nondiagonal element of the parametric emissivity matrix. The approach allows a description of the quantum statistical correlation properties (noise) of an adiabatic quantum pump.

We present the relation between the Floquet scattering matrix and the nonequilibrium Green’s function formalisms to transport theory in noninteracting electronic systems in contact to reservoirs and driven by time-periodic fields. We present a translation formula that expresses the Floquet scattering matrix in terms of a Fourier transform of the retarded Green’s function. We prove that such representation satisfies the fundamental identities of transport theory. We also present the “adiabatic” approximation to the dc current in the language of the Keldysh formalism.

We investigate the shot noise generated by particle emission from a mesoscopic capacitor into an edge state coupled to another edge state at a quantum point contact (QPC). For a capacitor subject to a periodic voltage the resulting shot noise is proportional to the number of particles (both electrons and holes) emitted during a period. The shot noise is proportional to the driving frequency, however it is independent of the applied voltage. If two capacitors are coupled to a QPC at different sides then the resulting shot noise is maximally the sum of noises produced by each of the capacitors. However, the noise is suppressed if particles of the same kind are emitted simultaneously.

A quantum coherent capacitor subject to large amplitude pulse cycles can be made to emit or reabsorb an electron in each half cycle. Quantized currents with pulse cycles in the GHz range have been demonstrated experimentally. We develop a nonlinear dynamical scattering theory for arbitrary pulses to describe the properties of this very fast single electron source. Using our theory we analyze the accuracy of the current quantization and investigate the noise of such a source. Our results are important for future scientific and possible metrological applications of this source.