# P14: Periodically driven quantum dots

## Project Description

The interplay of the influence of time dependent external fields and local correlations in nanosystems leads to interesting many-body physics. It can be studied in quantum dots, molecular single-electron transistors, and cold atom gases. Besides abrupt and adiabatic changes of system parameters periodic modulations with high frequencies are of particular interest (see also project P9). In such systems interesting phenomena like photon-assisted tunneling, non-adiabatic pumping or coherent suppression of tunneling processes can appear^{(1)}. Here we will develop methods which allow for a study of such phenomena in the non-perturbative regime (with respect to quantum fluctuations). To this end we will use two complementary approaches, the functional renormalization group (FRG) ^{(2)} and the real-time renormalization group (RTRG) ^{(3)}, with the help of which it has become possible in recent years to analyze the time dynamics of basic models of strongly correlated nanosystems at low temperatures. This includes abrupt changes of system parameters in the Kondo model^{(4)}, the interacting resonant level model ^{(5)-(8)}, and the ohmic spin boson model^{(9)} as well as adiabatic modulations for the interacting resonant model^{(10)}. In particular for the interacting resonant level model or, equivalently, for the ohmic spin boson model close to the coherent-incoherent transition^{(11),(12)}, it has recently been demonstrated ^{(7)} that only the combined use of both renormalization group methods leads to a detailed understanding of the time dynamics. The reason is that within the FRG method one expands in all interaction parameters whereas the RTRG approach can treat arbitrarily large local interaction but employs an expansion in the coupling between the local system and the environment. Furthermore, the RTRG method allows for an analytical understanding of the time dynamics. The two methods are based on completely different diagrammatic approaches and use different flow parameters. Whereas the FRG method uses the standard Keldysh formalism, the RTRG method is formulated in Liouville space and is a tool to analyze the kernel of kinetic equations for the reduced density matrix of the local quantum system. Both methods are very flexible and are capable of treating arbitrary time-dependent external fields. The aim of the present project is the study of the coherent-incoherent crossover for the interacting resonant level model in the presence of periodically modulated external fields with a frequency which is comparable or larger than the renormalized tunneling. Of particular interest are the conditions for which coherent oscillations can occur and to calculate the corresponding frequencies. Furthermore, we will study the suppression of tunneling processes and photon-assisted tunneling for this model and will analyze the realization of quantum pumps driven by the application of AC transport voltages for a model with two reservoirs. This project will profit from the progress in projects P11 and P16 and will provide important input for project P10.

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(12) U. Weiss, *Quantum Dissipative Systems* (World Scientific Publishing Company, Singapore, 2012)