System–bath entanglement theorem with Gaussian environments

Abstract

In this work, we establish a so-called "system-bath entanglement theorem", for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local systems, as long as the interacting bath spectral densities are given. We validate the theorem with the direct evaluation via the exact dissipaton-equation-of-motion approach. Therefore, this work enables various quantum dissipation theories, which originally describe only the reduced system dynamics, for their evaluations on the system-bath entanglement properties. Numerical demonstrations are carried out on the Fano interference spectroscopies of spin-boson systems.

Nonequilibrium system-bath entanglement theorem versus heat transport

“…Recently, we had constructed the SBET. [3,4] This theorem comprises exact relations between the entangled system-bath response functions and those of local anharmonic systems. Applications had been demonstrated with Fano interference spectroscopy.…”

“…Applications had been demonstrated with Fano interference spectroscopy. [3] The SBET had also been exploited in the establishment of the thermodynamic free-energy spectrum theory. [4] To extend this theory to the nonequilibrium scenario, we should include multiple bath reservoirs with different temperatures, so that heat transport is anticipated.…”

“…Theoretical studies have been mainly carried out in terms of nonequilibrium Green's function (NEGF) methods. [1,2] In this work, we exploit the well-established systembath entanglement theorem (SBET), [3,4] with extension to nonequilibrium transport scenario. Adopted here is the Gauss-Wick's environment ansatz [5,6] that is commonly adopted in various quantum dissipation theories.…”

“…These include the formally exact Feynman-Vernon influence functional theory, [7] and its derivative-equivalence the hierarchical equations of motion (HEOM) formalism. [8][9][10][11][12][13][14] While the existing SBET deals with for response functions only, [3,4] the extended theory is concerned with the nonequilibrium steady-state quantum transport current through molecular junctions. In this context, the extended SBET provides an alternative approach to the NEGF formalism.…”

“…In Sec. II, we present the well-established SBET for the response functions, [3] with extension to the nonequilibrium transport scenario. In Sec.…”