## 4. Coherent quantum dynamics and decoherence

The research program of the Burgd¨orfer group addresses the simulation of transport and decoherence in quantum matter. Coherent quantum dynamics as opposed to diffusive and incoherent classical dynamics is the hallmark of “quantum matter”. Design and development of novel functional materials inevitably involves the quantum nature of its constituents and quantum dynamics resulting from the confinement in space (low-dimensionality) or phase space (ultralow temperatures). One of the current challenges is the exploration of the classicalto- quantum-crossover, the delineation of the parameter space within which true quantum behavior prevails.

One focus is quantum transport through low-dimensional matter. Charge carrier transport through quantum wires and quantum dots is strongly influenced by quantum coherent behavior. One example of our current interest are nanoribbons of graphene, two-dimensional sheets of graphite with inscribed constrictions (“dots”) for novel functionalities on the nanoscale. With the implementation of the modular recursive Green’s function method (MRGM) developed in our group, transport through nanoribbons containing 106 graphite hexagones can be simulated. Another class of micro- and nanoscale systems where quantum coherent transport is crucial are normal-conducting super-conducting (S-N) hybrid structures (“Andreev billiard”) where the electronic structure and transport is governed by coherent particle-hole scattering at the S-N interface. The computational challenge is here to solve the Bogoliubov-de Gennes equation for quantum dots with non-separable geometry. A third class of problems currently under investigation are quantum dots with strong electron correlations interacting with anti-ferromagnetic coupling to Kondo impurities. Direct large scale diagonalization in optimized bases is required to determine the electronic structure and transport properties.

The fundamental limitation to coherent quantum dynamics is decoherence, the ubiquitous coupling of the quantum system to the environment that leads to irreversible dephasing and to a quantum-to-classical cross-over. The computational tool we have developed to treat open quantum systems is the quantum trajectory Monte-Carlo (QTMC) method. The reduced density matrix of the system is determined as ensemble average over stochastic wavefunctions propagated with the help of a non-linear stochastic Schroedinger equation.

Cooperations on decoherence and Kondo physics are planned with the group of Held. Synergies are expected with the J¨ungel group for quantum structures and quantum dots. Collaborations with DFT experts within the CompMat consortium (Blaha, Mohn, Redinger) on further developments of time-dependent density functional (TDDFT) codes are envisioned.