Chain representations of open quantum systems and their numerical simulation with time-adapative density matrix renormalisation group methods

Details Chain representations of open quantum systems and their numerical simulation with time-adapative density matrix renormalisation group methods Chain representations of open quantum systems and their numerical simulation with time-adapative density matrix renormalisation group methods

2011-12-29

arxiv.org/abs/1112.6280v1

In Uli Wurfel, Michael Thorwart, Eicke R. Weber and Professor Chennupati Jagadish, editors: Semiconductors and Semimetals Vol8

Physics

Quantum Physics

Book chapter

Scientific paper

This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour interactions. This mapping, carried out rigorously using orthogonal polynomial theory, then allows the full evolution of the system and environment to be simulated using time-adaptive density matrix renormalisation group methods. With the combination of these two techniques, numerically-exact results can be obtained for dissipative quantum systems in the presence of arbitrarily complex environmental spectral functions, and the correlations and processes in the environment which drive the effectively irreversible dynamics of the reduced state of the quantum system can be explored in real time. The chain representation also reveals a number of universal features of harmonic environments characterised by a spectral density which are discussed here.

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