Quantum entropy of systems described by non-Hermitian Hamiltonians
Zloshchastiev, Konstantin G.
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Copyright: 2016. IOP Science. Due to copyright restrictions, only the abstract is available. For access to the full text item, please consult the publisher's website. The definitive version of the work is published in South African Journal of Accounting Research, Vol 3. Pp 1-18. http://dx.doi.org/10.1088/1742-5468/2016/03/033102
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non-Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.
Sergi, A. and Zloshchastiev, K. 2016. Quantum entropy of systems described by non-Hermitian Hamiltonians. Journal of Statistical Mechanics : Theory and Experiment.