Research Publications (Systems Science)
Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/842
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Item Linear Quantum Entropy and Non-Hermitian Hamiltonians(MDPI, 2016-12-16) Sergi, Alessandro; Giaquinta, Paolo V.We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly consideredItem Time correlation functions for non-Hermitian quantum systems(American Physical Society, 2015-06-09) Sergi, Alessandro; Zloshchastiev, Konstantin G.We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semidefiniteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.