Generalized system-bath entanglement theorem for Gaussian environments
arxiv(2023)
摘要
A system-bath entanglement theorem (SBET) with Gaussian environments was
established previously in J. Chem. Phys. 152, 034102 (2020) in terms of linear
response functions. This theorem connects the system-bath entanglement
responses to the local system and bare bath ones. In this work, we generalize
it to correlation functions. Key steps in derivation are the generalized
Langevin dynamics for the hybridizing bath modes as in the previous work,
together with the Bogoliubov transformation mapping the original
finite-temperature canonical reservoir to an effective zero-temperature vacuum
via an auxiliary bath. With the theorem, the system-bath entangled correlations
and the bath modes correlations in the full composite space can be evaluated as
long as the bare-bath statistical properties are known and the reduced system
correlations are obtained. Numerical demonstrations are carried out for the
evaluation of the solvation free energy of an electron transfer system with a
certain intramolecular vibrational modes.
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