29 November 2023 to 1 December 2023
KEK Tsukuba Campus
Asia/Tokyo timezone

Automatic hermiticity for mixed states

30 Nov 2023, 17:15
15m
KEK Tsukuba Campus

KEK Tsukuba Campus

KEK, 1-1 OHO, TSUKUBA, IBARAKI 305-0801, JAPAN

Speaker

Prof. Keiichi Nagao (Ibaraki University)

Description

We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product IQ that makes a given non-normal Hamiltonian normal by using an appropriately chosen Hermitian operator Q. We studied it for pure states. In this talk we show that a similar mechanism also works for mixed states by introducing density matrices to describe them and investigating their properties explicitly. In particular, in the future-included theories, where not only a past state at the initial time TA but also a future state at the final time TB is given, we introduce a “skew density matrix” composed of both ensembles of the future and past states such that the trace of the product of it and an operator O matches a normalized matrix element of O⁠. We argue that the skew density matrix defined with IQ at the present time t for large TBt and large tTA approximately corresponds to another density matrix composed of only an ensemble of past states and defined with another inner product IQJ for large tTA. This talk is based on the collaboration with Holger Bech Nielsen [Prog. Theor. Exp. Phys. 2023 (3) 031B01] (arXiv:arXiv:2209.11619 [hep-th]).

Presentation materials