Time correlation functions for non-Hermitian quantum systems

KwaZulu-Natal Node, National Institute for Theoretical Physics (NITheP), South Africa(Dated: December 19, 2014)We introduce a formalism for time-dependent correlation functions for systems whose evolutionsare governed by non-Hermitian Hamiltonians of general type. It turns out that one can define twodifferent types of time correlation functions. Both these definitions seem to be physically consistentwhile becoming equivalent only in certain cases. Moreover, when autocorrelation functions areconsidered, one can introduce another function defined as the relative difference between the twodefinitions. We conjecture that such a function can be used to assess the positive semi-definitenessof the density operator without computing its eigenvalues. We illustrate these points by studyinganalytically a number of models with two energy levels.