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- Title
New method for merging several exponential operators' product into one exponential operator.
- Authors
Zhang, Chun-Zao; Fan, Hong-Yi
- Abstract
For two operators X and Y , which obey [ X , Y ] = τ Y + μ we shall prove e X e Y = exp X + τ Y 1 − e − τ + μ 1 − e − τ − μ τ , which means we want to merge two exponential operators' product into one exponential operator. This kind of operator identity is useful for calculating the quantum entropy S since S = − κ Tr { ρ ln ρ } , when ρ ≡ ρ 1 ρ 2 , but ln (ρ 1 ρ 2) ≠ ln ρ 1 + ln ρ 2 , thus the merging operator formula is demanded. In this way, several exponential operators' product can also be merged. We shall employ the method of integration within normally ordered product (IWOP) to derive the merging operator identity.
- Subjects
QUANTUM entropy
- Publication
Modern Physics Letters A, 2023, Vol 38, Issue 36/37, p1
- ISSN
0217-7323
- Publication type
Article
- DOI
10.1142/S0217732323501584