Automatic hermiticity for mixed states
| Autor: | Keiichi Nagao, Holger Bech Nielsen |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Progress of Theoretical and Experimental Physics Nagao, K & Nielsen, H B 2023, ' Automatic hermiticity for mixed states ', Progress of Theoretical and Experimental Physics, vol. 2023, no. 3, 031B01 . https://doi.org/10.1093/ptep/ptad025 |
| ISSN: | 2050-3911 |
| DOI: | 10.1093/ptep/ptad025 |
| Popis: | We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product $I_Q$ that makes a given non-normal Hamiltonian normal by using an appropriately chosen Hermitian operator $Q$. We studied it for pure states. In this letter we show that a similar mechanism also works for mixed states by introducing density matrices to describe them and investigating their properties explicitly both in the future-not-included and future-included theories. In particular, in the latter, where not only a past state at the initial time $T_A$ but also a future state at the final time $T_B$ is given, we study a couple of candidates for it, and 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 ${\cal O}$ matches a normalized matrix element of ${\cal O}$. We argue that the skew density matrix defined with $I_Q$ at the present time $t$ for large $T_B-t$ and large $t-T_A$ approximately corresponds to another density matrix composed of only an ensemble of past states and defined with another inner product $I_{Q_J}$ for large $t-T_A$. Comment: Latex 14 pages, typos corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phys |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|