Feynman path integrals offer a convenient and elegant tool for dealing with the statistical physics of quantum-mechanical systems. By using the Trotter product formula, one can evaluate directly the propagation of many-body quantum systems in imaginary time. The idea of an influence functional arises when one wishes to consider division of the physical system into a primary system and a bath. We present a general approach to the problem of constructing influence functionals, one that is capable of dealing both with Boltzmann baths (classical oscillators) and quantum baths of bosons or fermions. The fermion bath of special interest is generally a submanifold of the electronic state such as the bridge structure connecting chromophores or electron localization subunits which are common in problems of mixed valency and superexchange. The fermion bath is treated by a general rewriting of the influence phase S as a sum of an eigenvalue part SEV and a remainder, S0, that describes transitions. Reduction of the original Hamiltonian leads to a reduced Hamiltonian with effective off-diagonal matrix elements and influence functionals which can include memory effects. We present a general formalism for construction of influence functionals, and discuss particular applications to systems of interest, especially in electronic-structure problems. The following paper presents a variational technique for finding effective Hamiltonians.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics