Quantum systems interacting with bath

I will discuss two extensions of the standard theory of open quantum systems. The first concerns the heat current flowing through a system between two baths, quantified by its generating function. As shown previously the corresponding system functional has the form of the Feynman-Vernon influence action, but with a time shift in some of the kernels. For harmonic oscillator baths interacting with a qubit through a spin-boson coupling I will show how to compute this functional under the non-interacting blip approximation (NIBA). The generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. I will also discuss numerical examples showing rectification of the heat current. The second concerns a qubit interacting with a fermionic bath by a Frölich polaron coupling (one boson– two fermions), as an example of a non-harmonic bath. Since the path integrals are not Gaussian the Feynman-Vernon action cannot be obtained in closed form, but contains terms of all orders in the system histories. I will discuss the quadratic terns, which correspond to standard Feynman-Vernon theory, and the quartic terms, being the first correction. This is joint work with Brecht Donvil and Kirone Mallick, available as [arXiv:1911.00427], and with Jan Tuziemski [in preparation].