We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling two-level system. The time evolution is formulated and derived in terms of the density matrix of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing and vanishing population difference.

http://arxiv.org/abs/1207.4877
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

Non-Hermitian quantum dynamics can be defined by giving a more fundamental role either to the Heisenberg’s or to the Schr\”odinger’s picture of quantum dynamics. In both cases, it is shown how to map the algebra of commutators, defining time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The results and discussions are of interest to methods for simulating open quantum systems dynamics in terms of non-Hermitian time evolution.

http://arxiv.org/abs/1012.0906
Quantum Physics (quant-ph)