My current research:
In the context of research into the strongly non-markovian dynamics thought to drive efficient energy transport in photosynthetic complexes, a new many-body simulation technique that combines time-adaptive density renormalisation group (t-DMRG) methods and an analytical mapping of open quantum systems onto an effective infinite one-dimensional chain model has recently been developed here in Ulm. The mapping onto a chain is essential for the efficient application of t-DMRG, but it also provides a new and physically intuitive way of describing and analysing open-system dynamics at a microscopic level. Moreover, we also have recently shown that there is an elegant and powerful mathematical formulism that allows the transformation to be carried out analytically using orthogonal polynomials (OPS), and which also allows us to use many of the established results from the extremely well-developed theory of OPS to analyse non-markovianity and open-system dynamics by studying the properties of the chain representation of the environment.
One of the key observations made so far is that for all spectral functions in the Szego class, the chain energies and couplings are known to approach universal constants at large distances from the quantum system. From this we see that the particular characteristics of a given environment are essentially determined by the first few sites of the chain, and in this region the energies and hopping rates are generally rather non-uniform. On intuitive grounds, we believe that this nonuniform region is responsible for the non-markovian part of the open-system dynamics at short times, as excitations generated by the system-environment interaction cannot propagate freely away from the system and are scattered back towards it by the disorder in the chain. This is effectively a spatial representation of what are commonly referred to as environmental memory effects which, are responsible for an information flow from the environment towards the system. As the disordered region of the chain is of finite (and sometimes rather short) length, excitations eventually propagate into the uniform region and can subsequently propagate away without any scattering back towards the system. This effect describes the long-time markovian dynamics of the system and in some cases we also expect that this is where truly irreversible dynamics (spontaneous decay, energy absorption etc.) have their origins.
However, we have not yet explored in quantitative detail this intuitive picture of how these processes occur, nor have we related them explicitly to recently developed measures of non-markovianity and standard descriptions of open system physics in the usual system-reservoir picture. With the methods at our disposal, there currently exists a huge opportunity for deepening our theoretical understanding of dissipative physics and the quantum-classical boundary, as well as developing new and efficient methods of simulating complex open quantum systems. My current research objectives can be devided into the following set of overlapping investigations:
– A real-time story of dissipative quantum dynamics.
– Chain representations.
– Towards simpler simulations of non-markovian dynamics.
– Quantum vs classical environments.
– Building effective environments.